Depends on what you want. Males tend to be bigger, and lay around a lot. They are often compared to lap dogs. They have a more animal smell to them, but it's not strong or unpleasant. Males are around 500 to 600 grams or more.
Females are active, and generally don't like to sit still. They like to run around and explore when out of their cage. They are smaller, and have softer fur. Sometimes half the size of males. around 300grams for an average female.
Both make excellent pets, and it's really about how you want to interact with them.
Depends on the individuals, but usually no. Most get along very well. Constant fighting, or serious injury is pretty rare in domestic rats. Personally I've had more trouble with females in that respect - being more active they tend to piss each other off more I guess :?
My friend has one female rat and I have two males from the same litter. I've never seen (or heard) my boys fighting, and they are much more active than my friend's female rat. But then again it all depends on the rat and it's owner.
radical-- if the female is alone she may also be depressed. if it gets serious enough she may even try to commit suicide though of course being depressed doesn't necessarily mean she will try that route. rats are socail and most need at least one other rat companion. though there are always exceptions to the rule and the female may just be one of the lazy ones. they do exist, i have one myself.