A lot of the parts that you talk about having “play” are supposed to have play. One [of the many] kart-chassis tuning methods is to tighten and loosen brackets which attach to the chassis – or sometimes removing them all together. This includes floor tray, front-bumper bracket, side-pod brackets, torsion bars, seat brackets, etc.
Your chassis looks to be quite old as the side-pod bars do not mount perpendicularly to the chassis – that’s always a quick tell. That was standardized sometime in the early- to mid-2000s.