I'm not sure the number is constant. I think it scales with either the age or the prominence of the comment. I've seen threads where I was unable to downvote top tier comments, even though I could downvote their children.

It's constant at 501.

I did see interesting behavior when I crossed the threshold: I couldn't downvote comments that existed before I reached that karma level (or at least the UI didn't render them with a down vote button).

Downvoting wouldn't be affected by that per se, but downvote arrows last for a much briefer time window than upvote arrows do.

I think after 8 hours you can't downvote a comment anymore.

Are you sure you do not suffer from a mitm?