Thoughts (only read the OP in depth):
-Discards should not immediately be 24. At least the first round should be 12 or less. Even if they start at 24 in the second round that'd be fine.
-Salvages being increased but weighted based off market price is a very good idea.
-Relics for good rounds is good, but 4-1 and 5-0 should give the same amount of relics. Only giving it to 5-0 is going to lead to a rich-get-richer situation, whereas 4-1 can be gotten by almost any team if they're performing better than expected. This is a good way to reward weaker elements.
-I think something that should be considered for auction is 1-2 rounds of draft and then the rest auction. I know draft wasn't popular but a hybrid system has some strong points - it immediately gives generals a lieutenant to bounce off strategy with, it doesn't lose all the suspense auction has because there's more than 12 players worth drafting, and it could benefit weaker elements by slightly mitigating superteams.
-Alchemist good. Flexibility good. I like teams being limited to facing two generals for the same reason.
-I'm fine with Masters not being General and participating as a Soldier - times have changed, we want activity above all else - but they should be restricted from their element. EDIT: I should say why I think this - you can basically choose the person you appoint as General to be on your team and agree that they'll get you. That should be treated as a loophole, the auction system is supposed to prevent anyone from choosing the team they're on.
-Wrong mark should have never counted as an autoloss in the first place, so good.
As for hydras - I'm strongly opposed to them, as last War indicates. I think they're full of abuse possibilities, pose unnecessary complications, create unfairness, and are generally against the spirit of War. If I were more active here I'd die on that hill. But I'm not, so instead I'll try to be productive.
If they're going to happen, it needs to be public knowledge. Generals need to know that they're buying two people instead of one, so bidding can be fair. Players need to know they're interacting with multiple people. Also, I think it should be limited to 2 people per account, but if not, that number needs to also be public knowledge.
Related, a question - is the forum account required to also share only one game account for the purposes of War, or can each member of the hydra have their own game account? If multiple game accounts are allowed, those need to all be public too - I don't really think they should be but I wanted to ask regardless.