Do you have to install DOS 6.22 before installing Windows 3.0?

Windows up till before windows 95 is an operating environment - it runs on top of dos of some flavour (95 and 98 ran with dos, but once they were started, they took over a lot of functionality, and were much closer to a proper operating system. Unlike windows 3.x they were closely coupled to specific versions of dos, so no one ever thinks about it.).

You can run windows 3.x with pretty much any version of dos (except DR dos, iirc - windows actually checked for, and refused to run on it) - supposedly even freedos - see the bottom, dosbox or the ms dos start up floppy disks you can create from windows i believe. You can presumably also get access to dos with a technet subscription, assuming you need a licenced copy.

Windows 3.0 requires DOS to be installed as it's only an user interface or system extension, depending on point of view.

You will not require DOS 6.22, DOS 3.1 is fine, too.

Yes you do as Windows 3.1 is an application that runs under DOS