The sneezing thing.....my son had a pet rat Mikey and he would get raspy and sneezy when I put cedar chips into his cage. I had to switch to the regular pine. They didn't help with the odor, but I'm sure Mikey was allergic to the cedar ones.

I would put a divider in the cage or have a small container to put Chester in so he can eat. It sounds like both are males by their names and I'm not so sure two male rats would ultimately get along and as in any type of animal there is always a pecking order. It is your responsibility as their owner to be sure each gets his own share of food. You would do that with your children. You wouldn't let one starve because the other was older and stronger and stole the food. Maybe a seperate cage is needed. We purchased a large clear plastic storage box--like a rubbermaid container about the size of a laundry basket. We drilled holes in the plastic lid with a drill and it made a wonderful inexpensive cage and Mikey never got out. It was also easy to clean.