A system, comprises at least one of:
A
B
C
B becomes invalid after patent get granted and someone proves that in court.
1) Does this make the entire claim invalid or only the B item?
2) Can A, B and C claim priority to different dates?
The whole claim will be invalid. You could potentially file for a reexamination and add a claim to just A and C. That is one reason to spend the money on more dependent claims.
If you, instead of the "at least one" structure, had separate dependent claims for each element and had multiple priority documents that the application claimed the benefit of, then the individual claims could have different effective priority dates. The effective priority date on a per claim basis is something you would argue for during prosecution when a claim was rejected or would be argued during litigation or before the PTAB.
