Holding down materials is commonly done with strong neodymium magnets or honeycomb pins. If you search for those terms you’ll find a ton of posts on the matter.
I’m a die hard magnet guy but there are pin loyalists out there too.
As for settings, cardboard is covered like crazy. Search for “cardboard settings”. It’s tricky because cardboard varies so much. For typical amazon boxes I do 300 speed 80 power but there’s no substitute for testing.
I’ve cut balsa but again it’s hard to say. Thickness matters. Balsa cut super quickly though. Search for “cut test template” to see how other people have done material tests, here’s one such post:
Good luck and happy testing! Be careful with corrugated, it’s notorious for catching fire!