As far as diet is concerned, if you do a search of the forum you can find a lot of threads with "recipes" or models to follow. General rule of thumb is to always provide a high quality lab block made specifically for rats. (Harlan Teklad is very good, and you can order it online
. You should start with 2018 until age 8 months, then switch to 2014.) This should be supplemented daily by fresh veggies and occasional fruits. Here
is a great list of safe fruits and veggies for rats. I decided to make my own dry mix for my boys, which was always available for them in their food bowl. You can look up SueBee's diet for rats--that is basically what I did, except I eliminated the dog food, since they were already getting the lab blocks.
Sneezing is normal when rats are in a new environment. However, if the sneezing lasts more than a few days, or if it gets progressively worse (accompanied by red mucus around the nose/eyes, known as "porphyrin"), then you should keep a close eye on them. Get in the habit of listening to their lungs daily so that you know what they normally sound like. Rats are highly prone to respiratory infections, so it is important for you to be able to quickly identify problems when they arise.
What kind of a cage are you using right now, and how is it that he was able to catch his finger between the bars?
Also, you should definitely not separate the rats. They are incredibly social animals, and since they are already living together it would be cruel to split them apart. Rats who live alone for extended periods of time can easily become depressed and begin to have other emotional and even physical issues related to the depression.