Even if you pick adventure mode, you can still skip the cutscenes anyway by pressing pause then skip.
I'll play more of it later on since I'm going to talk to a few folks, but the most I've played of Freedom Planet was its SAGE demo (basically an expo for Sonic fan games, some of which are pretty good and better than what SEGA churns out sometimes).
The SAGE demo was alright. The framerate dropped sometimes and the physics didn't feel all there and the characters didn't stand out from backgrounds as much, but it made for a decent build on Sonic Genesis games. From what I've played of the release build today, they improved on the physics and the framerate is constant. The characters stand out a little more from their backgrounds, too. You collect 200 Power Crystals to get a 1-Up (and enemies can pick them up, but you can beat them up to get them back). It has a health meter, but you can replenish health by picking up Health Petals. You can also get elemental shields that do similar things to what elemental shields did in Sonic 3&K and Sonic Generations.
There are three different characters and some of them do similar things to what Sonic/Tails/Knuckles do. Lilac is basically Sonic where she gets a double-jump and she's the fastest of the three. Carol's kinda like Knuckles, so she can climb walls and melee attack... and she has a motorcycle for some reason i dunno. Milla can throw things at enemies and use a shield that reflects things at enemies.
I should disclose that a few friends of mine were involved in alpha/beta-testing and submitting ideas/music for the game from even before the game got kickstarted, so maybe I might be a little biased in favour of only what I'd played back in 2012.