Does a draw count as a title defense?

One guy shows up with the belt and leaves with it and the other guy shows up empty handed and leaves empty handed. This being the outcome of all draws I would say yes.

 

Yes.

In the early days there was a school of thought that a champion defended their title just by going the distance even if everyone agreed he lost but especially if it was close. This was motivated by the practical lack of centralized authority to decide who won a decision though. But we've got some champions with Losses counting as title defenses like Battling Levinsky.

If I had my way I would give a draw to the fighter with more overall points.

The bizzare scenario that we recently saw in the UFC is when a fight for the vacant title is a draw and the belt remains vacant.

 

Of course. If you didn't beat me (eg I'm the champion) why would you become the new champion?

And one anecdote related to this question.
When Bobby Fischer challenged Boris Spassky in Iceland in 1972, he needed 12.5 points from 24 games to become the new champion. Or to score 12.5 points earlier.
But when Bobby Fischer was supposed to defend his title against Anatoly Karpov, Karpov needed 12 (twelve) points to become the new champion.
Under the same circumstances, but the rules have changed. Fischer then stopped playing chess.

 

I guess