I have a business class ticket, issued by AA. The first leg was Bengaluru (India) to LHR on BA, and connecting at LHR to MIA by AA; the connection time was 100 minutes. (I believe MCT is 90 minutes for BA arriving T5 to AA connection at T3 -- don't ask, this was the only choice available).
My BA inbound to LHR was delayed by 30+ minutes, and I was told by BA staff to "run, you can make it" - and so I did, arriving at the AA gate 35 minutes before departure.
But when I tried to board, I was told BA had already re-booked me for LHR-LAX-MIA, arriving the following morning.
BA did not tell this to me, and I found out only when I went to the AA gate.
My assigned seat had been given away already.
I really did not want that, and a very resourceful AA person managed to make some calls, and found me the last business class seat - and I was one of the last one to board (20 minutes before scheduled departure).
All this happened two days ago.

Here are the problems.
(a) I have been given mileage credit for BLR to LHR (it posted yesterday) but not for the LHR to MIA flight (as of now).
This is just to give context, and the least of my problems.

(b) More worryingly, when I log in to my AA account, it still shows the original AA flight from two days ago, LHR to MIA, as yet to be flown.

(c) I also had to make a date change for the return segment (MIA-ATL, ATL-LHR-BLR), so I called in this morning.
After some effort, the agent got it done, but I still do not have a new ticket number - and I cannot find the new ticket number when I login, even though the new dates show.
I will be flying MIA-ATL in a couple of days and then from ATL-LHR-BLR after an overnight in ATL.

(d) When I login to BA website (because the ATL-LHR-BLR, yet to be flown, are on BA), it does show the two segments to be flown on BA along with the MIA-ATL yet to be flown on AA.
(The BA site also shows the BLR-LHR segment already flown - but even there the LHR-MIA is missing). I am able to select seats, etc.

(e) Of concern, even after the change in itinerary, the LHR-MIA still shows up as to be flown on the AA website.
When I assign a seat for MIA-ATL, that same seat number automatically shows for both the LHR-MIA and the MIA-ATL flights.

(f) Was then transferred to AA web support, and they claim no problems.They claim do not see the LHR-MIA flight on their side now.

Suggestions?
Thanks in advance.