I've become enough of an arrogant SOB evolutionary biologist poking his nose where it doesn't belong over the last year that I believe I have answers to all of these, and a few other important things to say.  WHILE MAKING IT CLEAR I AM NOT A VIROLOGIST OR IMMUNOLOGIST OR EPIDEMIOLOGIST AND THAT I COULD EAT MY WORDS IN THE FUTURE, though I have been pretty good so far.

How likely is it that the spread of this new strain was caused by a few superspreaders, and that most of the above is blown out of proportion

That would make sense if the frequency was rising in early introductions or when spread was thin on the ground.  Increasing fraction of the total infections while spread is already thick makes me think that there is more likely to actually be an actual effect on contagiousness.  They report a decent detectable increase in genome copy number as measured by PCR and sequencing in upper respiratory samples which makes me think this is likely.  More on the virology later.

What, uh, does the "71% higher growth rate" mean

TLDR: I think that it's probably barely 15% more infectious and the math of spread near equilibrium amplifies things.

I admit that I have not read all available  documents in detail, but I presume that what they said means something like "if ancestor has a doubling time of X, then variant is estimated as having a doubling time of X/(1+0.71) = 0.58X"

This can only be related to a parameter like R0 in relation to how much R0 has already been reduced by behavior changes to its effective actual R since the math gets really nonlinear and I presume I am either missing their math or there will be more detailed documentation in the future.  In the mean time let's run through an example.

I have seen estimates of 'generation times' for SARS-2 clustering around 5 days in the presence of all the stacked up behavior changes.  Doubling time is related to the generation time and the effective replication number Re, by the equation:

doubling time = ln(2) * generation time / (Re-1)

If you have reduced the Re to 1.1 with a 5 day generation time then you get a doubling time of 35 days.  If you have reduced it to 1.2 then you get a doubling time of 17 days.  In the former case, if you take 35 days to 0.58*35 = 20.1 days, you get Re going from 1.1 to 1.172, only 7% higher infectiousness.  In the latter case, if you take 17 days to 10 days, you get Re going from 1.2 to 1.34, a 12% increase.  Presumably the base R0 increases by a similar factor.

In short, the closer you are to equilibrium when measuring the effect the larger the effect a small change in contagiousness will have.  Given that compared to unmitigated situations we are pretty close to Re=1 and I never see cases doubling recently in Britain in less than two weeks, I doubt that the total factor of increase of infectiousness is actually all that large.  You get a huge nonlinear effect as you move the numbers around near one, even when the total factor of increase is not huge, but mitigation increasing by only a small factor can counteract it.

Prepared to eat this, hard, if I am misinterpreting what has been said.

Is there any reason to suspect this new strain might have an impact on vaccination plans? Are the currently approved vaccines (pick a country of choice to decide what this means) possibly better/worse/other against this strain?

It is almost certain that the vaccines (all of which present exactly the same piece of the virus to the immune system) work a bit less well on this variant, but at the same time I think it changes absolutely nothing important of substance for the near future.

For now, ignore EVERYTHING except the spike protein.  This lineage bears several mutations in this gene, responsible for fusing the virus to target cells and the main target of antibody responses (and a good fraction but not all of the T cell response).  They are, separated thematically:

deletion 69–70
deletion 144

 N501Y
A570D

D614G
P681H
T716I
S982A
D1118H

Deletion 69-70 and deletion 144 are in what's called the N-terminal domain.  This is not quite the business end of the spike but is near to it and is involved in invasion to some degree via mechanisms that are not well understood.  The double deletion has appeared independently several times, and seems to be helpful in becoming more invasive to human cells to some degree and also may help escape a subset of antibodies possibly as a side effect. Bit of a loooong story there I won't quite get into here.  Anyway, these are in a domain that constitutes about 20% of human neutralizing antibodies and are quite possibly somewhat immunologically relevant.

N501Y& and A570D are particularly interesting because they are in the receptor binding domain that actually sticks to ACE2.  In particular, N501Y has already been identified as a mutation that increases the strength of binding to the ACE2 receptor.  It also functions as a known escape mutation, and the other one could as well.

An escape mutation is a mutation that causes a subset of antibodies functional against the ancestor to become inert.  However, vertebrate immune systems generate a small quantity of a large number of antibodies against their targets, so generally speaking when an escape mutant comes along there are other antibodies around to take up the slack.

I  have seen papers exposing large numbers of recovered human serum samples against various escape mutations.  When one at a time was presented, only the weakest ~7% of responses (presumably consisting of the fewest antibody types) were affected at all and only a subset of those dropped below likely having an effect.  When two escape mutations were added, it went up to about 20%, still biased strongly towards the weaker responses.  But again, not all those responses dropped to zero, some just got weaker.  Of note, natural responses to the virus vary in strength by a factor of TWO HUNDRED, and a weak response is very different from a strong response.

I would expect that each escape mutation you add makes the fraction of responses that have a problem go up, and the size of the problem to go up.  We are talking 2-4 escape mutations here, so there is likely some immunological impact.

D614G is one of the first mutations  in the history of this virus from January and is likely associated with a mild increase in contagiousness to humans, via a slight change in the geometry of the trimer that is completely immunologically irrelevant.  

The rest of the mutations are in parts of the spike that are a lot less likely to be immunologically relevant, even if maybe one or two of them changes something about the arrangement of the three spike monomers  in the trimer that could theoreticaly affect binding or synergize with others to affect binding efficacy or shedding of the S1 domain from the protein or any number of other things, but dont necessarily and a bunch of them are probably just silent.

Given the sheer strength of responses created by immunization so far, as strong or even stronger than the very strongest natural responses, I find myself doubting that even multiple escape mutations will be able to break through the response to the vaccines.  I would presume they would make the speed with which immunization immunity decays increase, and mean that fewer additional mutations on top of this base would be needed to properly evade it.

But we will have do deal with this anyway!  It is now known that the human coronaviruses do evolve on a timescale of circa a decade to be able to escape previous antibody responses, we just constantly get exposed to these  new changes as they barely break through into us.  Over a timescale of somewhere in the single digit years, I would presume that this virus would evolve to escape immunity be it natural or vaccinated.  And there is a hell of a difference between getting infected when you are completely naive and have never seen anything like it, and when you just barely can be broken through into and you are still generating antibodies and T cells that both are still reactive, even if it can slip past well enough.  A vaccination rolled out to prevent this first burn through a naive population is vital, and we will see if we can keep ahead of eventual evolution with later boosters or if we just live in equilibrium with another respiratory virus which will not be like the current situation.

*****

This is where I nerd out randomly on something else.  Almost nobody is commenting on the fact that this lineage also contains a nonsense mutation in ORF8!  

ORF8, the 8th identifiable reading frame in the genome, is one of the several tricksy accessory proteins that the virus uses to subvert and confuse the adaptive and innate immune system both - in particular, it gums up the MHC complex that body cells use to present viral protein fragments to the adaptive immune system, both to train it upon first exposure and to tag a cell for destruction by eventual trained T cells.  This and other accessory proteins are almost certainly a large fraction of why this disease is so immunologically weird and causing such messed up immune responses in severe cases.

A nonsense mutation is a mutation that turns one of the codons that codes for an amino acid into a STOP sign, preventing the production of everything downstream of that position in the protein.  This nonsense mutation is practically right at the beginning of the protein, so functionally speaking it is obliterated.

This protein has, in the various lineages around the world, accumulated less impactful mutations at a faster rate than almost any other position in the genome, indicating that it is not under a lot of selective pressure to be maintained.  The accessory proteins are probably needed to replicate in bats, whose immune systems are tuned  differently than ours - their antiviral interferon responses are on a freaking hair trigger and their inflammatory responses are damped incredibly low.  They are probably a lot less necessary in other mammals.  A similar protein literally fell to pieces over the course of the first SARS outbreak twenty years ago, and multiple lineages have been seen with big deletions in this gene over the course of the SARS-2 outbreak but none of them became particularly common, and indeed several are basically confirmed to have died out entirely.

If NOTHING else, this lineage proves that the loss of the tricky accessory proteins is not a death sentence for the virus and the possibility of them being lost over time in the future remains.  This may be a mechanism of eventual self-attenuation, if previous research in Singapore indicating that the ORF8-deleted lineages were significantly less likely to send people to hospitals pans out (there was not enough research for me to be confident of this buty there were some reports that really need to be followed up on).  It is possible that this utterly broken ORF8 basically 'hitchhiked' alongside the spike protein changes that are likely responsible for increased transmissibilty, even if it is mildly harmful to the virus.  This virus does not seem to be doing recombination in the human population, so such evolutionary hitchhiking can become an important force.