simply put yes, it is not equal to 0. it is continous, it doesnt split at the end of the years

Not entirely certain but it definitely seems like you need to use integration.

Decay is constant, it doesn't just decay in chunks. Therefore your numbers for atoms 2 and 3 will be off because more of atom 2 has decayed into atom 3 than you are taking account for when you do it in chunks.

Also, atom 1 can never ever get to zero, it's half life not zero life.