1. I don't think so, but someone who flies them more could tell for sure. I thought EI discontinued all J to London and is basically operating like an LCC.

2. You look at the segment and not the ticket. Whether you chose the coach flight is immaterial. If you are flying in coach, irrespective of the reason, you're treated as if you're flying in coach. In that case, status would have gotten you in, assuming that the SNN lounge is operated by EI, or (as you put it) one of thirty different types of membership. It's very common, by the way, and not limited to just this type of ticket.

3. Yes, unfortunately you were wrong unless you had sapphire or emerald status on one of the Oneworld carriers. You said you used AA miles so that would be either Platinum or Exec Plat.

4. See #3. There is no one to explain to because they were in the right on this one.

I empathize with you, but they followed the rules. They could have bent them if they chose to, but that is purely at thier discretion which they chose not to exercise. If you have status then you have a legit complaint. Frankly, though, you will not be compensated. They will note it and maybe speak with someone about how to enforce the rules, but in the end that's probably about all they will do.