The MULE is the most useful unit in SC2, and a lot of people don't seem to use it during mid or late gameplay. I have listed all the units (works in multiplayer) that can be repaired by it here: http://www.edepot.com/forums/viewtopic.php?f=7&t=4924
Repairing stuff....nice xD The way your post is worded though... its like you're explaining sc2 to elementary-schoolers...
Ive seen mules be dropped into mineral lines or on other other siege tanks in TvT to force their opponents siege tanks to shoot each other or their own workers. Since I saw how useful that was I find myself watching replys going OMG drop a mule in his bioball and his 6 tanks will kill all the marines for you!!. The whole dropping in workers and stuff also kinda works for Overseer changelings.
Ya for changelings you have to drop 2 changelings the first makes the tanks face towards the changeling(cause he will morph before they attack) and the second makes them shoot but still the same effect.
I have used mules to repair thors when I am on the move, to keep the momentum I gained. It works really well but, I always have in the back of my head the fact that I just lost 300 minerals when I summon one to do that.
The only thing that gives minerals out of nowhere is the supply depot extension since it's free 100 minerals. The mule money are money that's there and will get mined out eventually, so don't feel so bad about it. If you have above 500-600 minerals at the time you probably don't need that mule so much anyway...