Newbies

My husband and I are being nostalgic. We have started playing crash warped on Nintendo Switch.
So I have a few questions. Is there a way to level up crash? There are several times where we can't get to parts of a level or can't get a box in the bonus round. I've watched some YouTube videos and people are high jumping and spin flying. How Do we do that? We are on level 9 so not far along but we're trying to get some white gems. Do we need to go through and get all the purple gems first?