To answer the first question, one would need to know the make/model of the motherboard. The second question is easy; before. You always want to update before you try the new CPU. Otherwise, you won't be able to boot in order to do the update.
I would update the BIOS anyway, just to be safe. The T5670 was launched Q2'08, the T9400 Q3'08. So they are quite close together. Chances are, they use the same BIOS. But I can't say for sure.