Getting a job while green card application is in process

[Bony]

I'm on a F-1 visa, and I'm getting married this month to a US citizen. I have a couple of questions about the process of becoming a permanent resident.
1) If I receive a work authorization while I wait for my adjustment of status, would I have any problems applying for and getting a job?
2) I'm taking my fiance's last name, is having different names on my passport and marriage certificate going to be an issue in this process?

[PraetorianXI]

1) Yes, you can apply and get a job, that is what the EAD (work permit) is for.
2) Not necessarily, did you file the forms with your new name or old name?