You are right, he likely smells so bad because of this diet and because of the filth he was living in.
Changing his diet will help a great deal with the smell. As time passes smell from his previous environment will go away. If the filth is in his hair shafts, it will take a bit longer but will gradually disappear.
Rats need very little protein, too much will slowly destroy their organs
That is why they need a good quality block low in protein like less then 16% protein, and 14% or less is better
If you are unable to get the recommended blocks locally, there are places it can be ordered from depending upon what country you live in (you did not put that info in your profile)
He bites though the bars because he is likely used to being fed through the bars
Do not put you fingers near the bars and never feed him through the bars
There are things you can do to help him get over this
You are right, he needs to be in the main room so that he gets lots of interaction.
Actually it would be good if he bites your cat because then your cat will be afraid of him and stay far away
No matter how gentle and loving your cat is, cats have instincts and will go after small things that move
so it will be much safer if your cat is afraid of him
Make sure that the cage he is in is extremely secure & sturdy, has small bar spacing, and is at least 4 cubic feet in size (at least 6 cubic feet in size if you are adding 2 babies) with a base of at least 30 in by 18 in and height with levels
He needs at least one other same sex rat to live with (babies or a spayed girl are the easiest to intro to an adult male)
This will not only benefit him, but will make him a much better pet
If you decide to intro babies, it would be best if you get two babies because babies need another baby to play with
Baby boys need to be separated from their mama and sisters at 5 weeks old (some people separate them too early).
They would need to be 10 weeks old before being physically introduced to him.
Since he is an adult, there are gradual intro steps that will need to be followed when introing rats to ensure no one is hurt.
Please read:
http://www.ratshackforum.com/forum/showthread.php?t=32368
Yes, the babies would be able to get out of a guinea pig cage because of the bar spacing.
They would need a cage with very small bar spacing because if a rat can get it's head through the bars, it can get out.