The operating airline for the affected services appears to be AA, so yes, 1) through to 3) - you need to go to AA for consideration. I would be optimistic on 3), you may get something for 2) but not for LAX, 1) I think is unlikely - you could have gone to Boston, but you couldn't in the timeframe and accepted another option. You may have been in with a shout if you had LAX-LAS-BOS as one ticket and BOS-TLV as another. So maybe better to open a dialogue with your insurance company about these issues. AA usual attitude is traditionally "there's bad weather, we got you there as quick as we could, a lot of people slept in the airport".

Ironically, you should have had no problem with the cosmetics and other essentials bought in London, that's BA's fault if the bag was booked to either LHR or TLV and normally they are sympathetic provided it's not Dior's latest.

BAEC process the Avios and TPs, but AA has to agree to them, a liaison process that goes via BAEC. Right now I guess there will be delays in processing this, you won't be the only one in this position.