I have a 1998 mazda protege lx it was a 1.5L, but when i bought the car it had 200,000 miles on it, i put a new engine in it and it was a 1.8L it runs fine and i feel like it has more power but my engine shakes alot and when i shift into drive the engine shifts or jumps, its not a problem right now but im just wondering what i could do to support it! its automatic

 

It sounds like you need new motor mounts. I bet one or more is broken on the rubber portion.