Hey man , you have not looked the firmware properly. First of all , US firmware on sammobile is always written as the country 'cellular south' . So , buddy on sammobile firmware section type p5210 and then look for the country cellular south . I was also confused first but then I found my tab's pda code and csc code and then looked for the country and it matched with cellular south . So buddy search for cellular south country . And if you don't want to download from sammobile or you have any problems downloading from sammobile , here is the link https://mega.co.nz/#!sJZCxQ7T!hdJXKX...WqgGQgmOz1DH3A
P.S. - It the latest US stock firmware for GT-P5210. And the link which darthjader has provided, the firmware is of any European country because US firmware starts from UEU. And the latest U.S. firmware is P5210UEUAMK1 . I have provided you with the link of latest P5210UEUAMK1 . And to the answer for your 2nd question , Yes, I flashed the pimproid rom without any glitches and problems. What I did was that my tab was rooted and TWRP was installed . I just placed the pimproid rom in my tab's internal sd card , booted into TWRP recovery and then without any wiping I just installed the rom because TWRP automatically wipes the data and dalvik cache . I haven't tried the grevious rom . Ok my friend , after writing such a long post I hope that you find my post useful .
PLEASE HIT THANKS IF I HELPED YOU .
Sent from my GT-N7100