Try cleaning caches of the apps (browser and facebook). If don't work you can try a factory reset (wipe: partitions data and cache, and dalvik-cache)
FB works perfectly for me (page at least). I don't use the official app (is very laggy), I use Friendcaster instead (and it work well).
did it and no solution, i just came back from my phone company, we did some test, we used my sim card in another phone and we had the same problem, so we changed my sim card to a brand new sim card, we put it on my phone but again the same problem, so we tried using that new sim card in the other phone we tried earlier, but same problem, wouldnt access FB from browser, so then we did the following, the other phone was able to access FB from browser using his sim card, then we put that sim card into my phone, but with same results, and here is the weird thing, when we put the sim card back to the other phone (the phone that belongs to that sim card) he wasnt able to access FB, but he was able to do it just before we tried that sim card on my phone, what makes me to believe, that my phone is putting up a lock or something to FB into the sim card, this is really new to me, and have no idea how to fix it, any ideas? in the mean time, gonna go back to SDSL V1.1 and see if problem still persists on that version.
Edit: Ok so i went back to SDSL V1.0 and im able to log into the FB app and into the web page, so problem is with V2.2, gonna try to go back to V2.2 and see if problem still persist.
Edit2: Ok, now i have the following problem, i cant go back to V2.2, i did a full wipe (following leoposas tutorial, when i went into fastboot i got a blue screen with some codes instead of the black screen, but it did the full wipe), in CWM when i install zip from sdcard (ROM + Kernel .35), it installs everything, when everything is done and i reboot the phone, i cant get pass the SDSL logo, i tried going back to V1.1, same thing happens, but this time it will bring me back to CWM, when i try to go to fastboot, i get blue screen that says ("Display initialized USB init ept @ 0x6b000")
Edit3:wow already 3 edits haha, anyways so i installed V2.0 by fastboot, because i couldnt do it by recovery, now i have the following issue, i went back to recovery to try and install V2.2, but i get the following error on recovery "E:Cant open /sdcard/xda-cm-7.2.0-SDLSL-11062012.zip (bad)" for some reason CWR cant open my sim card, i can use my sim card normally running V2.0 but every time i try to flash V2.2 it gives me that error, i already flashed it once, so gonna download it again, and see what happens, wish me luck!
Edit4: cant seam to be able to install ROM's by CWR, i would say installation complete, but when i reboot the phone, cant get pass the SDSL silver logo, then when i go back to CWR to try to re flash the ROM, i get this message "E:Cant open /sdcard/xda-cm-7.2.0-SDLSL-11062012.zip (bad)", at this point dont know what to do, really need help right now, currently flashed V2.0 by fastboot, and gonna use this one in the mean time.