About seat assigment. IB operated.
Non status : AA would do it on an IB flight (by phone), but IB will erase it later
When I was gold : They did not erase it the last time

Miles earning : It's the marketed branding that counts you'll get
100% mileage + 100% bonus on any IB/BA/AA operated flights with an AA or BA flight number
You'll get 60% mileage + 60% on any IB marketed flight not going to north america (regular discounted economy fares).
The only IB flights numbers you don't loose are the non-stop transatlanics from Europe to US/Mexico.
So AVOID IB marketed flight from LHR to TLV. Always use a BA or AA number to fly AA, BA, IB.

Any of those miles will count to elite status and to the 500-miles upgrades earning counter.