will amd fx 8350 cpu work with this "Asus M5A78L-M/USB3 Micro ATX AM3+ Motherboard" without any problems?
Yes although I wouldn't run a 125W CPU on it. Also looking at your part list get a new PSU asap since that Lepa one is likely a total train wreck.
If BIOS version is 1401 or more recent, Yes.
If not, No.
Are you buying a 8350 soon?
I already have the fx 8350