First

Does space and ground combat happen at the same time, just two different theaters? Also what happens if you win in one theater but lose in the other?

Second

If the Death Star is in combat, but is the last space ship in theater vs a bunch of ships - if the rebels do not have the cards to kill it, is the only option to run?

You alternate between rounds of Space and Ground. After both conclude each player can retreat if able. You can certainly win in one theatre but not the other. Nothing specefic happens except whatever ramifications might occur such as not being able to retreat ground units due to lack of transport.

And yes if you don't have the DS Plans your only option is to flee as given enough rounds the DS Wil destroy all of your ships and you have no way to damage it. The opposite is true of the DSUC.

So you do one round of space then one round of ground? Or do fight the space first, then go to ground? Do you have to win the space fight first before you can go to the ground combat?

So you do one round of space then one round of ground? Or do fight the space first, then go to ground? Do you have to win the space fight first before you can go to the ground combat?

Per the rule book:

Combat Round

I. Space Battle: Starting with the current player, each player performs one attack with all of his ships. [Admiral only]

II. Ground Battle: Starting with the current player, each player performs one attack with all of his ground units. [General only]

III. Retreat: Starting with the current player, each player has the option to retreat from the system.

IV. Next Round: If both players still have units in the same theater (space or ground), they resolve another combat round. Otherwise, the combat ends.

You do not have to win the space combat to resolve the ground combat. Your attacking ground units move directly to the planet right away.

you cannot retreat when fighting the death star?

you cannot retreat when fighting the death star?

No the Empire can't retreat if the DS is in System.

But the Rebels can retreat if they want after a round of combat.