I am expecting the beginner box in the post any day now. Will it work in a duo game where I GM a single adventure, and are the obvious adjustments I should be making to make it work? I want the player to succeed, but I want it to be interesting for both of us and so don't want to fudge rolls and stage unlikely rescues when things get too hairy.

It's possible. If you do run this for a single person, I would urge you to have the player select one of the lightsaber users. They're pretty effective combat characters, though the Kel Dor is pretty squishy.

The adventure was designed to have different types of characters shine. So there are social encounters, exploration encounters, and problem-solving encounters along with the combat encounters. I suggest playing an NPC to help fill some of the holes that the PC left open.

Thank you for the suggestions. I will try exactly that. Lighsaber user (if the player wants to play that character) with one or two companions.

Are the beginner adventure characters more powerful than generated characters? I'm tempted to let the player create a character to use in the beginner adventure, but perhaps I should then award them some extra XP or adjust the adventure challenges/encounters?

The corebook characters are generally the same power level as the beginner characters. The beginner characters are some times built "differently". If you try and rebuild them using the Core Rules, you'll sometimes find inconsistencies in their stats. It's a design decision to allow the characters to fulfill the purpose of the game and help round-out the party and allow more options.

In the case of Force and Destiny, the lightsaber users are a step above the others since they get a very deadly weapon right a way. Under the rules as written in the core rules, starting characters do not have the option of starting with a lightsaber by default.

If you and your player are comfortable with it, go ahead and have the player roll up a fresh character that they want to play. You could give the character additional XP specifically to go towards rounding him or her out so the character can be useful in more than one situation.