Walls and Ceilings - Plaster Repair

I started a plaster repair on some 3" x 3" holes. (Wire notch holes in a ceiling under a joist--metal plate protected) I used 5/8" drywall--screwed into the joist on each end. Then I mixed Sheet Rock 45 (thinking it will be somewhat stronger) taped the edges and floated the first coat.

1.) Would the mixed mud I used be ideal on the first coat, if not then what?
2.) Since the holes are so small could I have gotten away with no tape?
3.) Anything I could have done better?

Should be fine. You should always have some sort of tape over cracks. Personally for a hole of that size I would cut a 5"-6" piece of rock, then score the back side slightly smaller than the hole, removing the excess leaving the paper on the front using it inplace of the tape. Nothing wrong with the way you did it.

Thank You!

Right yourself a check... you're a Pro!

I usually always use easy-sand for those type patches.