can a primer work if it have one base pair difference from the template DNA,?

Answer 1

Yes it can and in fact this is a commonly used method to introduce a point substitution mutation into a gene sequence. The change should be located in the 5' end of the primer and will cause fewer problems in longer primers than in short (less than 15 bases) because it will have a proportionately larger effect on the melting temp in short primers.

Answer 2

It may work, especially if the mismatch is not at the 3' end of the primer. Remember that the mismatch will only be critical in the first cycle of PCR, because after the first cycle, every product will contain the primer sequence instead of the original sequence. So you might want to decrease the stringency of the first annealing step.