Priming Sugar - Raw or Cooked?

Is it sufficient to put corn sugar directly into the ale or would it work better (or equally well) to boil it with some water (making a simple syrup) first, cool and then add?
I'd think the second approach would make for a more even distribution.
But will the heating/dilution be a problem for creating carbonation?

Yes
Correct
No, the sugar is dead to start with.

Thanks David.

When I bottle, how full should I fill the bottle?

I don't bottle much, but most people leave about 3/4"

If you have a bottling wand, the best way is to fill the bottle all the way up, and the displacement from the wand in the bottle will leave the perfect amount of headspace.

I do have a bottling wand, so that sounds perfect.

Typically you would boil the sugar for a few minutes in water, you don't really need a syrup consistency. I don't bother cooling, I just dump it in the bottling bucket, coil my hose at the bottom to cause a sort of whirl pool effect with the beer and siphon it right on top of the sugar water. There is typically only a cup or 2 of hot water so it won't affect 5 gallons of beer temperature wise. I have had great consistent carb levels in all my beers doing this.

yeah. 1.5 cups or so of water. it won't be thick like a syrup and you don't really have to cool it down since 1.5 cups of 200 degree water will mean squat to 5gallons of 70 or below beer.

I do cool mine a bit...only takes a few minutes of a water bath to chill 1.5 cups.