I was wondering as a new GM. Do more experienced GMs use rules from all three books. If so, what parts do you use from them. Example would be the optional rule for minion formations (AoR GM screen booklet).

Use whatever is needed. The rules are all cross-compatible, so there's really no restrictions. If you're a fresh and not certain what you should work with, just start simple, then include the more advanced rules as you progress.

I use all the rules, but honestly there's very little difference. Rules like the AoR squad rules are circumstantial, so don't worry about trying to know everything.

If you know how dice pools are created, and how to adjudicate the dice results, you're 95% of the way there. Honestly, I haven't cracked a rule book in the last dozen sessions...and it's not because I know the rules so well, it's that almost everything flows from dice pools. Everything else should be on the character sheets so you can make the players responsible for knowing how their Talents work.

What every one else said! ^

As I prepare for the upcoming game session I typically think about how that session is going to go and then look up stuff that might come up during that session. That way the info is fresh in my mind and I can keep the action going without having to slow things down looking in a book.

Yes.

I'm trying to think of rules that are exclusive to one book. Beyond the Morality/Obligation/Duty thing, I cant think of any.

Yes. Other than the player narrative hooks the majority of rules are the same. F&D focuses more on the Force, obviously, but other than powers not in EotE or AoR there is nothing really new there.

Some specializations hook directly into Morality/Duty/Obligaiton, so you may have to make tweaks if one of your player chooses one of these specs and you aren't using that ruleset in your games.

Yep! I use whatever I can as long as it fits. Squads, barrages, docking clamps, all the force and gear, point defense weapons... all of it...

I'm trying to think of rules that are exclusive to one book. Beyond the Morality/Obligation/Duty thing, I cant think of any.

There are some gunnery options for Sil 5+ starships that only appear in AoR. Conversely, the rules for point defense weapons only appear in EotE.

Along those veins I think there is/are a side bar or two in F&D about using the Force, like Lightsaber modding I believe is one example.

In my current game one character has two sources of Obligation, one has Obligation and Morality, and the third has Duty (And might gain Obligation pretty soon depending on how their interaction with a Hutt goes).