You can stay, and you can continue to work, and you can leave and enter (as a non-visa national).

However, I think you are mixing up the EEA Family Permit and the residence card. The permit is only issued abroad, usually quickly, but only valid for 6 months. The residence card is only issued in the UK, the application takes about 9 months to complete, and it is valid for 5 years.

So pick your poison. The usual way is to apply for an EEA Family Permit before coming to the UK, and once here, you would apply for the residence card. You do not have to include your passport at that stage - it would just collect dust for 9 months.

 

thsths, I am very sceptical about 9 months you are referring to. It seems we have some forum members here who are waiting for 12 months already.