Can I run cable line through studs
Yes. You can run low-voltage cable TV (RG-6 or whatever) cable pretty much anywhere you want.
any ideas on how to move my boxes from down low to up behibnd the tv.
If you also want to move your electrical receptacle(s) up behind the TV, the best way would probably be to not move the existing box, but drop some Romex (NM-B) from a new box behind the TV to the existing box below. Then connect the new wiring to the unused terminals on the existing receptacle unit. (If both sets of terminals are used, you'd have to pigtail the wiring, providing you don't over-fill the box..).
A clock receptacle fits the bill perfectly for behind the TV (they sell 'em at Home Depot). There are plenty of nifty looking cover plates for your low-voltage stuff, but I just used something like the plate below and had the cables running through the holes. It's hidden behind the TV, so doesn't matter if it's ugly. You could even just go with a hole in the drywall.
I did a quick search and found a couple of threads here on the subject. Maybe not exact answers to your question, but should give you some ideas..
http://www.diychatroom.com/f18/clock-receptacle-2682/
http://www.diychatroom.com/f18/home-theater-install-couple-electrical-qs-15387/
jerryh3's idea isn't a bad one, but it can look messy if you're planning on having a bare wall below the TV. There would need to be a jumper cable between the supply and load receptacle from the kit. It may be the better solution if you're not comfortable attaching directly to your existing circuit.