Tigerclaw

Is leveling up done in secret, or should the table know which card has been added and removed from each deck? For example, can a Tigerclaw player know her opponents' attack types and whether they changed them this level up, or is it all hidden in the moment?

Follow the rulebook. It specifies the exact order for leveling up, and what constitutes hidden information. You need pages 4, 15 and 16. TLDR: you cannot see what others picked when you are picking upgrades.

How long does Tigerclaw's poison token stay? Does it go back to the reserve at the end of the round?

Page 8, third paragraph.

Do tokens like tigerclaw's poison or Bain's marker get removed at the end of the turn?

Check Page 8, paragraph 3 of the rulebook.

If someone is attacked and has 1 card left in their hand and can’t play that card because it has no defense listed on it, but they’re surrounded by friendly minions that reduce the damage to 0, do they die?

Which version of the game you are playing? I don’t recall cards without defence action.

When arien uses Gush of water in GOA1, if Tigerclaw uses dodge to protect himself, does Tigerclaw move 1 space back ?

Can you attach the images of the cards involved please?