If I repair a face up card it is flipped to facedown. If I repair a face down card it goes into the discarded damage deck. Since the number of damage cards represents the number of hull damage, how do you keep track of your “true” damage if the card is now in the discarded damage deck?

If I have 1 shield & 3 hull and I have a facedown damage card that I can repair next action. I get stung by 3 hits, which reduces my shield by 1 to 0 and reduces my hull by 2 to 1. At this point I have four facedown cards going into the next round. Next round I choose to repair the actionable facedown damage card, adding this card to the discarded deck. I still have 3 damage cards. Another player can see that I have 3 damage cards and with my 3 hull would think that I have 0 hull and that my ship is destroyed. But n reality I still have 1 hull left. Am I thinking of this correctly?

No.

A ship is destroyed when it has damage cards assigned to it currently, equal to its hull value.

A discarded damage card is no longer assigned to the ship, and doesn't count towards the cards needed to kill it.

Ships don't have hit points.

Also, you don’t take a damage card for a “shield hit”, so at the end of that attack you’d only have two damage cards, the two that went into the hull.

That’s what makes shields so powerful: if your opponent roles a crit, and you have a shield to absorb it, then you don’t take the face up card, you just lose a shield.

Just remeber that regular hits are dealt with before critical hits. Again to your example, let’s say one of the three hits was a crit: the first hit would go into shields, the second hit into hull, the crit into hull, face up.

OK, just for clarification

If I have 1 shield & 3 hull and I have a facedown damage card that I can repair next action. I get stung by 3 hits, which reduces my shield by 1 to 0 and I take 2 hits, which results in me getting 2 damage cards. At this point I have 3 facedown cards going into the next round (the 1 existing facedown damage card plus 2 more from this attack.). Since the number of cards matches my hull of 3 I’m destroyed.

At that point you have 3 facedown damage cards and are destroyed and removed at the end of the initiative step of the ship that shot you, or immediately if the damage occurred outside of the engagement phase e.g. from a Proximity Mine.

There's no 'going into the next round' once you're destroyed, unless a specific ability saves you (e.g. Tel trevura's ability).

It's very simple. If the ship has damage cards equal to its hull value assigned to it, it dies. You're reading way too much into this.