No Slim or Super Slim can play PS2 disc game. Now you can run PS2 Classics (emulation) on CFW PS3, but compatibility is around 80%.
Only FAT PS3 (specifically the one with EE, launch model), has 99% compatibility. FAT PS3, however, is lot less reliable than Slim or Super Slim.
Advice: Play PS2 games on PS2.
I saw some Slims PS3 (i like slim) with CEHC 20xxx and 25xxx but i try to avoid looking for those because you said it can MAYBE be downgraded.
But if Firmware is important, why should i look for serial number, i should look for firmware version, right?
By the way since im buying used PS3, and if firmware is important, not serial number, than i can yust ask the man who is selling PS3 what firmware they are on, is that correct??
Oh and by the way, i was thinking...PS3 has hard drive right..so why do i need to buther with the drive, i can just transfer games straight to HDD,
why do i need disk drive.
And also, that PS2 games thing on PS3..can they also be played from HDD??
If this is similar to Wii who run games from Extarnal HDD except GC games.. so if i understand correctly, i can run PS3 games from HDD but i need Disk drive to run PS2 games..or...right?
Nope, this is in-house Sony emulation. Basically Sony published a few PS2 games on PSN under the name PS2 Classics. Hackers found out it is PS2 game wrapped in an emulator. What hackers have done is to replace the game portion while still retaining the emulator portion. With that, you can run PS2 games on any PS3.
So it's basicly like PSX games on my PSP?
But that means i can run any PS2 games if i modify it with some software on PC (like "PSX2PSP" for PSP)
And by compatibility, what do you mean?? You mean net running correctly or not all games can be played? 
