Check the existing cable for markings. RG6 or RG59? RG6 is preferable and most likely what the cable installer used. If existing is RG59, then install new cable.
Terminations are specific to the cable type/size. Inexpensive tools can do the job, expensive ones are faster and more convenient.

10-15 feet of coax (even RG59) in good shape isn't going to make a whole lot of difference. Crappy connections and the wrong splitters will be more problematic. I assume we're talking about an regular broadcast antenna (and not a satellite dish).

I'd just hook it up and see how well it works. The first thing I'd make sure is that I've got the splitters wired up right if you still have them. Make sure that you're using the in and out in the right direction. Make sure that you do not have more terminals on the splitter than you are using. Also older cable TV splitters may only be good to 600MHz, you may wish to upgrade them to the 1000 Mhz ones (all easily available at the home centers or electronic stores).

Actually, your concern over 10-15 feet, as well as the concerned raised over RG59 v RG6, is lost in the noise level over your attic mounting.

Attic mounting can easily have a 40-50% signal loss over roof mount. Things such as siding, foil back attic insulation, roofing materials, and your neighbors house can have a significant effect on reception. With digital broadcasts, this is even more of a concern since it's either make-it or break-it.

As far as the coax, just use what's there and see what you get. You may need a pre-amp at the antenna or distribution amp at the distribution point if feeding multiple televisions. But, I would highly recommend a rooftop mount unless you're only 20-30 miles from the antenna farm.

Pulling the wire up with the connector intact sounds like a good plan, and will also leave me enough wire to roof mount the antenna should the reception be poor inside the attic. I'll definitely heed the advice on the splitter/pre-amp.

Thanks everyone!