Work

Are the pays for work fixed? I mean for example, easy work gives 490(?) bux, tough gives 990, and hard gives 1980.

It's because one of my monsters worked as a mailmon and it gave me 1980 bux, while the others only 990.

Does the stat affect the bux gains?

If your monster has a high level in the stat being raised, it does the job easier, thus resulting in more pay. So in your case, that monster has a very high agility rating so he did well as a mailmon, which raises agility.

So...is it advisable to raise only one stat for a worker monster?

Yes it is. Unless you plan to use it for combat. Which wouldn't be odd considering you've got the SRP for it in the first place.