GA pilot reported experiencing a near miss and observing a near miss in the traffic pattern at a non-towered airport.

Narrative

It was a busy morning at ZZZ as there were 5 planes in the traffic pattern. I was on departure leg XX (left traffic) and Aircraft Y was coming to enter left traffic for XY and was making non standard calls and a non standard entry. I turned left downwind and the pilot was also on left downwind (I saw him on my Sentry). I asked what his plan was and didn't know his intentions. He mentioned something wrong with his alternator. We were too close; so I made a right 360 for spacing. The pilot was above another plane (Aircraft Z) on short final XX and was preparing to land; they must have been 200 feet from each other on final. Aircraft Z called a for him to go around and Aircraft Y went around and then landed on rwy XY. I ended up going around and off set to the East. I called Aircraft Y to make sure everything was OK because it wasn't super clear if it was an emergency for him or not. Overall no one got hurt but it was a close call. I wanted to submit this report to ensure pilots are making the right calls at a busy non-towered field and establish the important of strong communication in potential emergency situations.