Could meloxicam be used to treat gout?

Yes, it can be used. Meloxicam specifically hasn’t been studied in gout, but its drug class meloxicam is in have been shown to be effective to reduce pain and swelling during gout attacks. Note: they treat the symptom of pain but not they do nothing for the underlying cause - the gout itself. If you use it for gout, loop your doctor in; longtime use can erode the stomach and gut lining, leading to ulcers and bleeding.
Not a good choice. Theoretically yes, but in practical terms there are several much more effective therapies. I would never prescribe Meloxicam to treat gout.
It could be used. To help reduce the swelling and hence pain associated with gout.