Hello and welcome!
1) Turtles require a ton of water, so unless you are eventually able to have 240 gallons of water or two 120 gallon tanks, i suggest you stick with just one little guy.
2) That tank is not nearly big enough. Turtles require 10 gallons of water per inch of shell. So if your turtle is an inch and a half right now, it needs at least 15 gallons of water, but it will need much much more soon. So my suggestion is to go out and buy the biggest tank you can afford, and let the turtle grow into it. If it is a female it can grow to be up to 12 inches, so 120 gallons.
3) The reason it is probably not eating is because of his conditions. When I first got my RES in one of those small plastic dishes, he wouldnt eat, but as soon as I got him into a bigger tank with a heater and the water at the correct temperature (78 degrees), he started eating like mad. Also throw some veggies in the water and let them sit there, he may eventually munch on them.
4) Im probably not the best one to answer this question, but i know many people on this forum do take there turtles out to walk around the house and what not. I personally dont because I am in college and live with roommates and would rather not deal with that risk, plus i can only assume it stresses him out a bit.
5) The basking spot is very important to a turtles health and shell growth. The temperature needs to be 91 degrees and you need both UVA and UVB lighting, which means two seperate lights, but in the meantime any light will be better than what you have, just to get him to get out of the water and bask. You can buy basking docks at any petstore or many of us on here have made there own. Here is an example of one that I made for my turt.
http://www.redearslider.com/forum/viewtopic.php?t=13621
that is a pretty elaborate one, but its just to give you an idea. There are many different ways to make one, so have fun with it.
6) Like I said previously, at least 10 gallons of water for every inch of shell. Basically you can never have enough water for them. They are most comfortable in the water, so whatever you can give them they will be fine.
On top of all that you are going to need a very powerful filter because turtles are very dirty animals, and there water needs to be kept very clean.
I think that may be everything. Im sure somebody else will see something I missed and fill you in.
I wish you and your turt the best of luck, they are wonderful animals and great companions.
Oh! and if you could post some pictures of your turtle that would be wonderful, everybody here loves to see what everybody has.
Justin