Congrats on the "graduation"! It's very exciting! But I know what you mean about wanting to stay with Cooper. Becky was so fantastic and I didn't want to leave. I was with them for far longer than you (had some issues with P4 and placenta taking over) and it was so hard to cut the apron strings!
1. Technically there is no medical reason to be seen sooner than the next 2 weeks but if you want peace of mind and are anxious to get those early OB discussions going then don't feel bad about asking to be seen sooner.
2. OB u/s practices vary. Some are due to OB preference and others due to insurance. My OB's office has a travelling sonographer who comes in and does the u/s. I had all my u/s done in office by her. However, a friend of mine who is also a patient of the same OB had to go to an u/s facility for all her u/s because her insurance would not cover them if done in-office. So it really depends. I'd first find out what your insurance will cover before making final decisions on OB based on this.
3. How far along were your other 2 miscarriages? You very well may be fine with seeing your standard OB. At your first OB meeting you should have the discussion about bringing in perinatology care (a.k.a MFM - maternal-fetal medicine).
4. Can't help with this one...I'm in northern NJ. But I'd ask Becky if she could ask Dr. Cohen for a recommendation.