50%. With current knowledge N is either 100 or 99 with an equal probability.

No, the chance of it being red is much higher. If there's one green ball in the jar, than all previous draws would've needed to avoid the green one. The chances of that happening are way less than 50%.

Initially there is an equal chance that there are 99 or 100 red balls.

But if there is a green ball, it is unlikely to be the last picked. So the fact that you saw 99 red balls makes it unlikely there is a green ball.

This is a fantastic follow up question. The last ball is overwhelmingly likely to be red, though this is very counterintuitive. The “all-red” urn and the “all-red-but-one” urn were equally likely to be chosen at the start. But the draws have given you a lot of info about which distribution you’ve been drawing from. Were you sampling from the all-red distribution, your draws would be totally unsurprising — you would observe a run of 99 consecutive reds 100% of the time. If you were you sampling from the all-red-but-one distribution, however, you’d only have observed this outcome 1/100 times.