I have a 2005 Ford Focus and whenever I start the engine or accelerate the engines moves

Just as above the engine moves noticeably up and forward in the engine bay, I haven't noticed any unusual vibrations or clunking, could this be the lower motor/torque mount, or is this normal for this car?

Excess movement suggests a broken mount.

Extremely worn engine mounts

An engine mount is broken or the bolt holing the mount is loose Replace the broken mount. If this is too expensive for you, get a tube or two of silicon and apply it at least an inch thick after cleaning the mount thoroughly, then let it dry for 3 to 4 days

Rock the car back and forth while watching the torque mount to see how much play is in it or if you can see any separation.