Can donating eggs correlate with infertility in the future?

No: At this time there is no evidence that donating eggs leads to infertility in the future. Most women use only a fraction of their eggs during their lifetime and the rest if not used end of degenerating over time.

Not that we know of: To the best of our knowledge, it does not. The eggs that are removed are eggs that would have otherwise been lost. The eggs that remain in storage in the ovary should be unaffected unless there is some sort of a complication such as infection.