Okay if it's a Xenopus then yes get that little guy to a 10 gallon ASAP.
If the arm is broken just leave it alone, Xenopusare known for being quick healers, so it will heal on its own. Do you have any idea how it broke though? Remove any decoration from the aquarium that may have caused this. There's no magical food to mend a broken bone but you'll want to keep reptomin in the diet since that has calcium, may want to just skip the beef heart, frogs don't eat cows. I would recommend using reptomin as a staple that's mostly what I feed my frogs.
Temperature should be 68-72F, I personally keep my ACF at around 70F (cause that's what my AC is set at).
To answer your other questions, yes blind frogs can still find food, maybe a bit slower though -- no competition if kept alone means your frog will get his food just fine. They use smell and 'feel' things in the water more than they use their sight. Honestly I think they use their eyes for spotting predators more than anything.. when my Xenopus go on the hunt (I keep molly fry and ghost shrimp in my tank which they snack on -- albeit slowly) it's always in pitch black darkness at night.. so they don't seem to use vision as much as other senses to locate prey.
Since 10g is about the minimum for an adult xenopus I would't recommend any tank mates, could try some ghost shrimp though, I keep ghost shrimp with my frogs they eat excess food and they themselves provide a snack to the frogs now and then -- they're also only 30 cents or less usually to buy.
Oh by the way if you don't have a filter make sure you get one, for a 10g I would recommend a Tetra Whisper 20i (internal filter, very gentle). I use a Tetra Whisper 40i and a Marineland Penguin 150b for my froglets on a 20g tank (moving to a 40g breeder soon), so that is a lot of filtration and the frogs don't mind it at all.