1. You need to submit 2 copies of each, one for your daughter and one for you. However, be careful, there are other forms also. You need to complete G325A for yourself, for your daughter, and your wife needs to complete one too. Your wife also needs to file an I864(affidavit of support) for you and one for your daughter. You also need the medical form - one for you, one for your daughter. You also need a lot of supporting documentation, photos etc. Go through the checklist from the interview printout carefully, as well as through the instructions of all the forms.
2. This is up to you --- you may maintain valid H1B status until you receive the GC ---- that way you can travel and work based on that. If you see future problems with your employer, you may want to file EAD. Remember, however, once you receive the EAD and you sign the I9 with your employer, signifying the change, you are no longer in H1B status, and would also need to get AP to travel.