1. i'd use the 39. if it's in good shape, no need for a new ring. you'll probably need new bolts as a single ring will be thinner than the two you've got on there now. probably about $5 for a set at your lbs. if you're spacing out the rear hub, it doesn't really matter whether you go inside or out - whatever's easiest to get a good chainline.
2. with a 39 on the front, i'd do around a 14 in the back. i run 42/14 on my fix and it's just a little hilly here. the lower gear would probably be nice.
3. probably don't need a tensioner, as long as you can clamp the rear wheel down securely.
4. fixie folks like bullhorns and mustache bars for the extra torque they can get with the different hand position (at least, that's why i've used them). that said, you'll probably be fine with the drops you have. try 'em and see if you like 'em.
that's my $.02