Congrats on the deal on the Kay. Considering they've been going for twice that on Ebay, that's a bargain.
1. Yes, an adjustable bridge is great. I would definitely get one.
2. I've been hearing a lot of things about K&K stuff having problems on
www.rockabillybass.com except for the Big Twin. You should check into the Clef Revolution Solo instead. It's a simple bridge wing pickup that is very inexpensive, sounds great, and hardly ever feeds back. $99 at
www.uptonbass.com. It's simple, doesn't need a preamp in most amps, and has gotten excellent reviews on here.
3. Don't know.
As for strings, I personally went with plain gut G, D, and A with a wound gut E because the plain gut E just makes a thump with no sustain at all and I like a little sustain. I went with plain guts for the rest because I like their full sound and lack of that metallic clankiness. If you're going to slap rockabilly, it's much easier on your fingers. And it sounds really nice for jazz pizz, too. Some people complain of bowing problems with guts, but if you don't plan on doing any, then I think guts are where it's at. If you want a little more of a metallic sound, then you could try Eurosonics or Innovations, which are rope steel covered in nylon.