GA pilot reported two incidents involving near misses in the traffic pattern at SOP non-towered airport. In the first incident; the reporter was on final approach when a light transport flew in front of them for another runway. In the second incident; the reporter had not yet cleared the runway after landing when a light transport landed on the same runway.

Narrative

Incident #1: I was flying the RNAV 5 approach into SOP for practice. I called an 8 mile final on UNICOM when established; then again at 6; 4 and 2. Shortly thereafter Aircraft Y crossed from left to right maybe 500 feet in front of me and 200 feet below according to my ADS-B display which I had been monitoring. Aircraft Y had called that he was 10 [miles] out heading for an extended left base for [Runway] 5 after I reported a 4 mile final for [Runway] 5 and I assumed that was what he intended to do. Instead when he crossed in front of me he was less than 2 miles out from 5 on a heading of roughly 100 degrees. I came up on UNICOM and told him that he had crossed the final in front of me. His response was 'Sorry; I missed your call'? I wonder how he could miss all four calls? Aircraft Y then announced he was entering a left base for 23. I landed uneventfully. If I could see him on my ADS-B he could certainly see me!Incident #2: I was flying the RNAV 5 approach into SOP for practice. I called when established about 8 miles out. At about 4 miles Aircraft Z called 'GPS 5 inbound to Moore County; any traffic in the area please advise'. I advised 'Aircraft X inbound GPS 5; 3 and 1/2 out; full stop'. No response. I was monitoring his position on ADS-B and the interval was closing rapidly to less than 2 miles. Again since I could see him he could see me. I repeated that I was on a less than one mile final. No response . I kept speed up until I hit minimums; 200 feet; then dropped full flaps; chopped power and with hard brakes made the first turn off rather than touching down at the usual GPS/ILS touchdown zone. As I was completing the 90 degree turn but had not yet cleared the runway I saw Aircraft Z touch down about at about the midpoint of the runway. If I had had a mechanical issue and been unable to expedite my exit from the runway there would have been a collision.This behavior is unsafe but typical of the Part 135 & 91 charter/fractional turbine traffic around SOP; particularly on weekends. Most of these guys are cowboys; have little if any understanding of uncontrolled (excuse me; 'untowered') airport operations and seem to think they have right of way and priority at all times. Unless something is done it is only a matter of time before a serious accident happens and our airport management could not possibly care less; their sole interest is increasing the traffic count and selling more Jet A.