Hello! As far as playing on their backs, Sass frequently plays in this position on the top of her cage (I purchased an awesome playpen from Etsy last year that is priceless as far as entertainment value). It always makes me smile to see her upside down, her little chubby thighs pedaling a million mile an hour. Her house (cage) is parked right next to 2 GCC and I have wondered if she copied them because they both frequently play and sleep on their backs. Anyhow, it can't be anything less than good times as far as trust goes!
Sass also didn't quite know what to do with toys either when she first came home with us. I introduced her to many various types of toys and textures. At first she acted like they were unwelcome guests in her cage! She loves nuts, so I would wrap a nut in paper, clearly letting her see me doing it and pretty soon she caught on to that. Then there are those rope hanging balls stuffed with colorful paper. I hung one up in her house and "played" with it myself while she observed. Never one to miss out on the fun, she soon joined in. Now her favorite things to destroy are little foot balls stuffed with colorful paper, any king of cardboard, paper, those "natural husk balls", paper towel rolls stuffed with treats and tied up with twine.
I find Etsy has some incredible toy makers for very reasonable costs. It seems once they get the hang of what toys are for and their roll in toys, many birds quickly come around. I now rarely get "that look" (the one that is like stink eye and disgust at the same time) when introducing brand new toys, most of the time she rushes over to snatch them out of my hand! Just be persistent!
And don't forget other types of toys as well. I mainly focused on foraging and/or destroyable toys at first. Now I include metal clanking toys, shiny beaded toys, intelligence toys, physical toys (swings, ropes, ladders). stretchy plastic toys. Who knows what else. At first I figured I had lost my mind when I gave her a "pots and pans" toy that is quite loud, but she seems to confine her banging on that one to manageable hours
Good luck!