It's not subject to basis limitations.
However, most credits (including the credit for FICA tax on tips) result in a disallowance of the related deduction. This increases your ordinary income, which increases your basis, and also increases your nondeductible expenses, which decreases your basis. So the net effect generally is that it's a wash, although you can have some interesting side effects depending on how big these items are and how the ordering of the basis items affects everything.
Also, you mentioned being non-passive: The credits are still allowed for passive shareholders, but the credit allowed is limited on Form 8582-CR to the portion of tax attributable to the passive income.
I'll let someone else comment on at-risk limitations.