Trainee pilot reported an NMAC while flying in the traffic pattern at a non-towered airport. The trainee was on base leg following another landing aircraft with a fast moving twin on a long straight in final. The student; feeling the spacing was too close; crossed the final approach course and turned up wind to reenter the pattern. The trainee started a crosswind turn to reenter downwind. Looking left during the turn the trainee stated his surprise; the twin having gone missed; was straight at the trainee.

Narrative

I entered the traffic pattern at around TPA for ZZZ (1148 ft.) using a standard 45-to-midfield entry for Runway XX. The pattern was busy; with Aircraft Y ahead of me on downwind; a plane that had just turned crosswind behind me; and a number of planes holding for takeoff. I announced my location and intentions using standard phraseology; indicating that I was behind Aircraft Y and would follow them in.As I completed my GUMPS check and came abeam the numbers for XX; I heard a call for a plane on a 'long 7 mile final approach'. I don't remember hearing the type. As I approached my turn to base; I was monitoring the plane already on base; and looking for the plane on final. Before I began my turn to base; I identified the plane on final; which appeared to be above the horizon and several miles away. I also verified that Aircraft Y was established on final and descending.While I was flying the base leg; my attention was occupied by the normal workload of maintaining a stable approach; monitoring the plane ahead of me; and listening to the radio. As I neared the point where I would normally turn to final; I heard the plane on final announce that they were two miles out. The plane ahead of me took much longer than I anticipated to land; and I began to feel crowded. I decided that it was unsafe for me to turn final; as I did not feel confident that the plane ahead of me would clear the runway safely before I landed; and I was surprised by how quickly the other plane on 'long final' was approaching.With this decision made; I next had to figure out how to safely extricate myself from the situation; and called that I was exiting the pattern off of the base leg. I flew northwest until I was well clear of final; then turned upwind. I observed that there were still several planes waiting to take off; and I reported that I was flying upwind with the intention of rejoining the pattern on crosswind behind departing traffic.Right after I turned upwind and was studying the traffic on the ground; I did hear but didn't fully register that the pilot of the fast-moving 'long final' plane had called that he was going to go-around and was side-stepping to the right. My attention was on the departing plane so that I could time my re-entry to the left pattern; and after I visually verified that the departing plane was climbing straight out and would not be a factor; I began my left turn to crosswind. As I began the turn; I looked to my left and was shocked to see a twin-engine plane just aft of my left wing; at just about the same height and only several hundred ft. away. I immediately pulled a hard right turn and descent; and observed the other plane climbing and turning left into the crosswind. I continued to fly upwind for several miles to completely clear the pattern airspace; collected myself; and then rejoined the pattern for an uneventful landing.Contributing factors and Considerations: * Busy pattern at a non-towered airport * Nonstandard pattern entry by a fast-moving plane. * Heavily-accented English spoken by the pilot of Aircraft Z; infrequent and unclear radio calls * My failure to identify type and performance characteristics of the plane on final before committing to the turn to base * My failure to maintain situational awareness about the position and speed of Aircraft Z after it side-stepped to go aroundIn hindsight; given the uncertainties of the situation; I should have just extended my downwind in order to gather and process more information without the pressure of the landing workload. Additionally; my decision to leave the pattern off of the base leg and then attempt to rejoin from the upwind further contributed to an unsafe situation. I think that it would have been better to just leave the pattern; even though it was a nonstandard exit; and then rejoin via the 45 to Runway XX after safely transiting the airport.