1. I'd advise using brand new cables. In fact, if it was my bike, I'd replace the cable housing too. Fresh cables and housing will "crispen up" your shifting. It'll also make the replacement process faster and easier. I'm betting your old ones have a stray wire or two. If so, threading those used cables through the housing etc. will be a pain. Cables are cheap. Incidentally, one of the best bicycle tooling investemts that you can make is for a decent pair of cable cutters. I much prefer Shimano cable cutters to Park. Some guys use a Dremel with a cut off wheel. If you try to use ordinary diagonal cutters, the cables will usually frey.

2. You're absolutely correct.

3. Right again. With the shifter and the derailleur both in the smallest sprocket position, pull your cable taut and anchor it to the derailleur. You'll have to fine tune the cable tension with your barrel adjuster, but if you do it right, it shouldn't take very much additional fiddling.