How long it takes to get work authorization after filing marriage based GC?

[axient]

Hello fellas,

Thanks in advance for replies.
I am a F1 student getting married to US citizen after almost 2 years being in relationship. I have few question regarding marriage and GC processing.

1) How long should i wait after getting married in court before filing for GC?

2) How do i prove the validity of my marriage (to prove that it's not a GC fraud) while applying for GC?

2) How long does it takes to get work authorization after filing GC?

3) If work authorization gets processed, is it valid to work for any company in any US states?

Thanks,
Sakya