will the engine from a 2003 chevy cavlier fit in a 1998 cavalier?

This would be a lot of work. They switched the 2.4 liter engine in 1999, so after that, it's touch-and-go as to which engines would fit prior cars.

Yes

Will engine from 1998 Chevy Cavalier fit into a 2002 Cavalier, (both 2.2) ?

Will a motor from a 1998 cavalier fit in a 2002 cavalier

Yes it will. They all use the same motor. You can swap heads ECT as well.