The Argentines would have to get extraordinary lucky to sink both Hermes & Invincible, because they only had 5 exocets, it's doubtful a single exocet would be enough to sink these large ships, and if one ship was sunk the other is not going to hang around. Furthermore Hermes was kept a very long way back from the Falklands - I believe out of Argentine range AFAIK.
Bulwark was definitely surveyed in 1982, and the government even went so far as to announce it would be reactivated. It wasn't however because of the poor condition of the ship. I don't know how poor - it's worth remembering that it did actually do some service even after both fires, as recently as 1980 - so it seems doubtful that there was anything that couldn't be overcome if the need was desperate enough.
Apart from Illustrious, the British also had Ark Royal, which was launched in 1981. Of course, launch is a long way from commissioning, and in OTL, Ark Royal wasn't commissioned until 1985. Maybe this could be significantly sped up, although I think commissioning anytime in 82 is probably pushing it (?)
As far as American carriers, yes it was mentioned in the press, but it's unlikely unless the crew comes too - no RN crew would be trained on the ship, and converting would take a lot of time. Also AV-8As never served on an Essex, and the US carriers weren't fitted out for harriers (no ski jumps - don't know what else might be required).
Incidentally if the Argentines are significantly more successful with Exocets, and get some more of them, I think the most likely consequence is the British attempt Operation Mikado - the plan for the SAS attack on the Super Etendard base in Rio Grande. Assuming the attack isn't a total disaster, the plan was for the SAS troops to escape to Chile - but what they didn't know is the Argentines had several Marine battalions nearby who had orders to pursue any attackers into Chile. So either the SAS suffer a disaster, or maybe the war expands to include Chile.
Interesting thanks. I tend to agree that with only 5 air launched excoets the Argentines would have to have been very lucky to sink even one carrier in war time. Then again if the torpedoes on their modern sub had actually worked taking down a RN carrier in war time becomes a little more plausible.
I'm still curious about what the RN would have done with Bulwark if they had come to the conclusion she was worth reactivating. (ie would they have sent her south with the task force or kept her in reserve or maybe used her as an assault ship.) I doubt we will ever know what the answer is.