Snorri

How does Snorri’s ultimate interact with his gold and other tier 3 cards (except green)? Most of them state: "If a rune is active..." If two runes are active simultaneously (via his ultimate), can I resolve the effects of both active runes, or must I choose only one to resolve (similar to green)?

Follow the card text verbatim. If it says one rune - that means one rune. If it doesn't say to choose one rune, then it's not limited to one rune.

Is there a general rule against discarding two cards from one enemy action? After obtaining his ultimate, can Snorri use his green card twice on the same hero to force them to discard two cards — making it possible for a single hero (who also has two attack cards left) to force another hero to discard four cards in one round?

I believe you played Snorri's TIII green card incorrectly.

Can snorri gold horn hit a hero at range 2

Repeat - yes. The main target - no. Follow the card text.

Do you consider Snorri's active runes when copying their cards as NebKher?

Nothing in the card text suggests that you don’t.

Snorri’s Oath of Defense has a defense main action and the text “this turn: you are immune to enemy actions”. Can you play it as your primary action just to receive the immunity, without using it as a reaction defense?

Please check Defense[Defense]action section in the rulebook. And the [DefenseSkill] Defense/Skill action on the same page.

For Snorri's green card, can I block whenever the horn rune is available, or does it have to be the turn where the horn rune is down to use the free card when attacked?

You can only block whichever rune is currently active. Refer to the silver card for what an active rune means.