What Booster Gold is able to do without the suit. Dan Jurgens has stated in interviews that he hasn't revealed all the backstory for Booster for a reason. For future stories and such. (I believe from the Gold Exchange by Russ Burlingame. I'd have to go through them all to know for sure.) Still some of it has been hinted at if not mentioned in passing. I'll add to it more but if there's something you think I should add let me know.
History Student: I'm putting this here because far too many readers seem ignorant of this fact. It may be because some see Boosters' façade more than who the character actually is. Or simply that some writers make him seem kinda of dim. But the truth is it was a subject he took seriously, the reason he didn't know more about the past was because history isn't always exact. Facts are hidden or forgotten over time. It's also been canonically state that history wasn't Michelle's greatest subject.
Gymnastics/Possible martial arts training: This was more hinted at than shown in the comics and thus is mostly looked over. In Booster Gold #18 VOL.1 Booster is shown training on a pommel horse with skill that'd impress Dick Grayson. Even suggesting he'd make the Olympics, something that seemed entirely possible. Jurgens has shown Booster preforming some interesting moves in his art that hint at him knowing more extensive fighting than we assumed. When asked he confirmed that the character had more training since he was interested in such things.
Advanced Computer Skills: The first time I recall this being mentioned was in CTIF when Booster told Ted that since he was from the future that made present day tech primitive to him. Whether this was true or not wasn't sure at the time since Booster seemed to take over computer duties just to save Ted. Much later at the end of Booster Gold Vol. 2 he finds himself in an altered world and makes the same claims about the systems in present day being easy for him to hack. Only this time he actually does it and is able to get into government computers undetected. This however isn't the same type of tech savvy as Rip Hunter being able to create a Time Sphere. For one thing the time spheres were supposed to be hard to perfect and for another building things without directions has never been Boosters' thing.