General aviation pilot reported a NMAC on final approach caused by an aircraft that turned in front of them. Pilot performed a go-around and the same aircraft then caused another NMAC.

Narrative

While on a straight in final about 3 miles out for Runway 30 at Merced (MCE); another aircraft called 'turning base' and turned right in front of me. I went around immediately and offset to the right side of the runway so I could keep them in sight and stay clear.After the go around; I told traffic on CTAF that I was extending my upwind. I stayed on upwind longer than usual and climbed to about 400 feet above pattern altitude because the other pilot hadn't been responding to any of my calls and I wasn't sure what they were going to do next.On my MFD I saw them departing and climbing behind me at roughly my same altitude; and it looked like they were converging on me. To stay clear I turned right and started descending. While I was maneuvering; I realized the Class D airspace northeast of Merced was nearby. I double checked my position on the MFD; made sure I was below and clear of her; then turned left to stay away from the Delta boundary. It's possible I briefly touched the edge of that airspace while avoiding them.I realize how important it is to stay flexible; communicate clearly; and maintain full awareness of traffic and nearby airspace; especially when I notice that another pilot isn't following normal pattern procedures.