I did a quick search to see if these scenarios had been covered before and didn't find any thing

1. How does Greedo interact with the Direct Hit damage card?

Greedo reads "The first time you attack each round and the first time you defend each round, the first Damage card dealt is dealt faceup."

The direct hit card reads "This card counts as 2 damage against your hull."

Does this mean that Greedo would bypass shields if the direct hit card is the card dealt face up by Greedo's ability? If the damage does bypass the shields and the ship has 0 hull I assume it is considered destroyed.

2. If an ship with the R5 astromech uses the astromech ability to flip a direct hit card facedown does the ship regenerate one hull?

R5 reads, "During the End phase, you may choose 1 of your faceup Damage cards with the Ship trait and flip it facedown."

Does this mean that Greedo would bypass shields if the direct hit card is the card dealt face up by Greedo's ability?

You don't deal damage cards if the target has any shields left, Greedo only comes into effect when the target has no shields.

2. If an ship with the R5 astromech uses the astromech ability to flip a direct hit card facedown does the ship regenerate one hull?

A ship never loses hull, the rules are that a ship is destroyed when it has damage cards that equal the value of the hull.

Since a direct hit counts as 2 damage cards, if it gets flipped face down, then it only counts as 1 damage card.

1. How does Greedo interact with the Direct Hit damage card?

Greedo reads "The first time you attack each round and the first time you defend each round, the first Damage card dealt is dealt faceup."

The direct hit card reads "This card counts as 2 damage against your hull."

Does this mean that Greedo would bypass shields if the direct hit card is the card dealt face up by Greedo's ability? If the damage does bypass the shields and the ship has 0 hull I assume it is considered destroyed.

Greedo never bypasses shields.

Here's how the Greedo card works:

• You fire at an X-Wing (3 hull, 2 shields) and roll 4 normal hit results and a critical hit result.
• The X-Wing rolls its green dice and gets a single evade result
• You compare results as normal, so the evade result cancels on of the hit results
• You then deal damage as normal
  • ​First, we deal damage from the normal hit results
    • The first hit that was not cancelled removes 1 shield token
    • The second hit that was not cancelled removes another shield token
    • The third hit that was not cancelled deals a facedown damage card to the X-Wing, since it no longer has any shield

      This is when Greedo triggers! Since it is the "first time you attack" and it is "the first Damage card dealt", it is dealt faceup.

      Apply any effects of the faceup damage card as normal.

  • Then, we deal damage from the critical hit results
    • The uncancelled critical hit result deals a faceup damage card to the X-Wing.

If all the hits the ship equipped with Greedo lands on a target take off shields and no damage card is dealt, Greedo has no effect.

2. If an ship with the R5 astromech uses the astromech ability to flip a direct hit card facedown does the ship regenerate one hull?

R5 reads, "During the End phase, you may choose 1 of your faceup Damage cards with the Ship trait and flip it facedown."

You never "regenerate hull". You accumulate damage cards until the number of damage cards exceeds your hull value.

A Direct Hit says that it counts as 2 damage against your hull. You do not deal a second damage card to the ship. You simply keep the Direct Hit faceup and count it as 2 damage. So, if you have 2 facedown damage cards and a faceup Direct Hit, you have suffered 4 damage against your hull. If R5 is used to flip the Direct Hit facedown, you no longer consider that card to be worth 2 damage, and you now have 3 damage against your hull.

So, yes, you do kind of "regenerate one hull", but it is important to understand the correct way damage cards and hull points interact.

Lets say you roll 3 hits and a crit with gredo and your opponent has only 1 shield and did not cancel any hits with green dice or evade tokens. Here is the hit order.

1. This first hit will be resolved on the shields taking off 1 shield token from the defender.
2. With no more shields a hit will deal a face down damage card but with gredo in play that card would be flipped face up.
3. this is a regular hit and Greedo had already triggered so this would just be a face down damage card
4. with all regular hits resolved you move to critical hits. This would be a face up damage card delt to the defender.

Now with R5 and direct hits it allows you in the end phase to flip one critical hit face down. So yes it can flip direct hits assuming that it didn't take damage equal or greater than its hull value.

Example gold squadron with 3 face down damage cards on it. Lets say it suffers a critical damage. If it gets just a console fire you can flip it face down in the end phase without having to use your action in the following turn. However instead of one of those cards it was a direct hit the damage on the Y-wing will = the hull value so it will be removed (after any simultaneous fire opportunities if available) and R5 will not have a chance to flip the direct hit to face down.