Pilot reported a missing several ATC calls; experiencing a NMAC; and flying into airspace without authorization.

Narrative

My first time in the Phoenix area. It all started on down wind; left traffic. There were several airplanes in the pattern (maybe 5) I was behind a much slower airplane and let the controller know that I was faster and was told to 'do what you need to do'. The approach speed of a Aircraft X is 120 to 110 kts.; over the numbers at 90 kts.; touchdown 80 to 85 kts. What I 'needed to do' was to step to the outside of the plane in front of me and extend my downwind so I wouldn't overtake the plane in front of me on final and that's what I did. On final the Controller had a Aircraft Y in right traffic? turn base into me. I immediately started climbing anticipating a go around when I saw her on my screen flying directly at me and getting very close. The Controller immediately realized the mistake and asked the Aircraft X to turn left; she responded but didn't comply. I listened to ATCLive and heard the Controller ask me three times to then turn left. The first two requests were stepped on and I didn't hear his request until the third time. The Controller then asked me to fly out 6 miles and report back in. Not giving me a direction of flight I assumed downwind. When I was attempting to figure out where 6 miles was I flew into Glendale's airspace. The Controller immediately informed me and I made a 180.