I think he is lying. His story doesn’t make sense. Unfortunately it’s more likely that he ended up sleeping with someone who accidentally ended up pregnant. Like you said, why would he want to be in the child’s life if he really was a sperm donor? Not to mention the other concerns you brought up such as his age which is not ideal for sperm donation.

There doesn’t seem to be many benefits to the relationship. It seems like it’s just a pain and a burden. Not only because of the issues you’ve had with him but the very long distance further puts a huge strain on the relationship. It doesn’t seem worth it at all.