Fixed it, the problem was from fastvoip side. Thank you RonR for all the help!
As soon as I could make calls from my PC using a softphone using fv credentials, I could also dial the numbers successfully from my handset (**2 001 10_digit_USA_number).
Also, in the fv username I just had to provide 'username' and not 'username@fastvoip.com' (a mistake I did earlier). And it works with registration on [Voice Services -> SP2 -> X_RegisterEnable : (checked)]
So the final configuration is
Service Providers -> ITSP Profile B -> SIP -> ProxyServer :
sip.fastvoip.comVoice Services -> SP2 Service -> X_ServProvProfile : B
Voice Services -> SP2 Service -> AuthUserName : (Username)
Voice Services -> SP2 Service -> AuthPassword : (Password)
OBiTALK SP2 status says "Registered (server=193.67.131.157:5060; expire in 29s)"