so I replaced temp sensor couple weeks ago and it raised cold idle up to almost 1400rpm, warmed up idle 700-750rpm for a day and then somehow the computer adjusted back to 1200rpm, and I still have warmed up idle at 600rpm, then my fuel pumped arrived along with the filter and strainer, so I tried to replace those but realize the filter wont fit coz I have no way to fix it in place, anyway the new pump didn't make much of difference, car feels slightly faster on lower rpms but idles the same. it definitely looks like fuel related though, with full tank I can start the car easy, except say if I went shopping for 20mins and back even the engine's still hot and tank's full it'll took me at least 5sec to start and it'll suffer from very low idle even die right after, crank again everything's good, but if I only left for 5 mins and back, start the car it'll not have this prob. When the tank is 3/4 full the cold idle drops to just above 1000rpm, and when the tank drops to 1/2 full, idle drops to around 800-850 and the engine's shaking left and right. the car has only 144xxxkms, so I'm not too concerned about the fuel filter, also the stock strainer was pretty clean as well, so the next thing is the fuel pressure regulator, but it looks like it's in the tank, now I'm more inclined to believe there might be something wrong with the ecu.

 

Is there any live data you get from a scantool on Long term fuel trim (LTFT) and the Idle signal and TPS and post it up here? LTFT would tell you what the ECU has adjusted in terms of fueling.
Also are you able to check if the EFI relay is operating properly? It may have a delayed operation due to extra resistance either on the switch side or contact side of the relay. This EFI relay feeds the fuel pump ECU and the engine ECU.
It will also be worth while to check if the engine ECU is switching the coils and injectors during that start problem.