How would the "cable guy" route the new cable? I think you could probably do it yourself with more care to its appearance. Can you run the cable inside the wall, from your new room down to the basement? If so, you could just connect the new cable to the old one. If you want to keep the old one active, then use a splitter.

Your cable company will run a new cable for you, but it will cost you $$$. Its not real hard unless you need to snake a new cable down an outside wall.

Yea you will just need a couple of coax Female to Female couplers (we call them coax barrels in the trade) and then get a pre-terminated coax patch cable the length that you need it. You will have some signal loss with each coupler, but as long as the run isn't super long you should be fine. If you want to run the raw cable and try and terminate the coax yourself Home Depot or Lowe's sells are the parts you need to do so.

Not sure who your cable provider is. But DirecTVs "wireless" genie setup works really well. If your moving a cable network modem I would always suggest hardwire (physical cable) over wireless. Regardless it is always better to have cable connection rather than wireless. To many variables with wireless even with the advancements in today's wireless.

When I had wireless-G, the PS3 would stutter when trying to stream video. I hard-wired and no stutter. Went to wireless-N, and no stuttering at all either.