I believe that 2+2=4, but two earplugs with two earplugs make three will not convince me 2+2=3. It will convince me that something is wrong between my abstraction of 3 earplugs and the number 4.

Of course, I agree that an unfalsifiable belief doesn't deserve to be a belief, and yes, I can imagine a situation where I would believe that 2+2=4 is false: the collapse of Peano arithmetic.

Yes, if you ask me what kind of proposition would make me believe implies , my answer is that would be an instance.

Yes, the truth/falsehood in the formal realm has nothing to do with the physical realm, but no, believing that a true proposition is true would require interacting with the physical realm. The sentence has multiple meanings. It is true (modulo Peano axioms) in the formal realm. It is a belief in the physical realm. Some people believe it, others don't. I can imagine a situation that I'll be convinced to believe that this is false, but such situation would probably be strong enough to also convince me to believe that Peano arithmetic is inconsistent.