Yes look into a tank ! UVB is a must for any size turtle indoors ! To get a turtle under a UVB one needs a heat lamp this entices them to bask. I would not depend on "room" temperature because a babies basking area needs to be 90* and the water temp at 80* ! A turtle needs to thermoregulate it's temp and room temp does not allow this. So both a heat bulb and a UVB bulb is need. Stay away from full spectrum bulbs they are inadequate for turtles ! With babies growing so fast they need proper lighting more so , this will help prevent bone disease , helps digestion , helps metabolism of calcium ...
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http://www.redearslider.com/light_sources.html http://www.redearslider.com/lighting_issues.htmlThe water is to shallow even for babies. If they fall on there backs will never be able to right themselves and drown. Two to three times the shell length would be safer. Myself have always set a tank up for babies at the adult size tank , saves on all those up grades over the years. That's a 150 gallon tank with 18-20" water even for a baby , been doing it like that over five decades with no problems. BUT I do offer "lots of resting spots" all over the tank if they get tired not just a one basking dock. As I said that's how I do it to save lots of money over time. Not everyone may be able to do it but you for two babies you do need a larger tank. Ten gallons of water alone per inch of shell ! Yes this give more room to swim but it more for you to be able to control the waters parameter's alone with a filter.
Look at top header on this page and study all the links provided, especially the lighting and basking section.
The claw looks like old wound , not a problem. It will do fine if it does not grow back.