Hi Regoods,
Hope you've already fixed this issue but to add answers on these questions:
1. You can hide/disable the Availability filter by simply removing that code section from the filter code settings or by adding hidden: true, under name: 'Availability',
2. If you add hidden: true, under the name of the dropdown you want to remove, that'll hide/disable that dropdown from displaying. However, the filter's category dropdown uses the same data as Squarespace default category filter, it's practically works the same but with more flexibility, so not sure what you mean.
3. Are you using the the universal filter's sticky option and the mobilePanel? Your position: sticky might be getting overwritten so maybe try using an @media{} query or !important on your CSS code.