Yes Yes and Yes! I used to march with the Rebel Legion and 501st in the parades (A-Wing!), and lots of the Jedi guys/gals would head back into the park with their gear. Even us Pilots would have a pilot day when we rode the Star Tours ride - really awesome to do, with lots of photo ops for us! Lots of people are there in Jedi costumes/w lightsabers even! - it's totally normal.
The only rule is don't be a jerk about it. Like, don't go swinging your saber around, or signing autographs as "Luke Skywalker" or anything. Basically, same rules as
MNSSHP.
Keep in mind two things:
1. It's usually hotter than Tatoinne for SSW, so you might want to consider not wearing the heavy robes that the Jedi wear.
2. If your costume is super-accurate than you might not want to wear it at the parks where it can be damaged or have to carry a lot of gear (saber and such) because it can be heavy.
Usually for MNSSHP I would wear my Haunted Mansion tightrope girl costume. But that includes a huge crinoline, umbrella, crocodile, wig (heavy) and caplet (which never stays put!). Now I'm a mommy, I have to figure out something lighter!