Could invisalign work for cross bite?

Depends on severity: If dental, tipped teeth, invisalign can help correct crossbite but not as well as braces. If crossbite is skeletal, a side-to-side bone size discrepancy, correction is beyond the limits of clear aligners. In growing children need expander. In adults need expander coupled with sarp, surgery to release the two halves of the upper jaw that have fused together. See qualified orthodontist.

Possible but: Possible for cross bite but other devices may be needed.

Depends: on how severe the crossbite is. Only an orthodontist who sees your actual bite will be able to answer definitively. Most provide free consults. Go see one.