it stated that Full installer was dated May 31st and update installer had no date. Which is the latest June major update that you referred to?
Yes. The version on the site is always the latest one, you cannot download an outdated version from our site. The actual installer is probably even newer than that.
And what if it doesn't work with VISTA? Will I somehow be able to go back to my Dec update version that still works (but with some bugs)
You will have to uninstall everything from FSDT, then reinstall everything, using all outdated installers and you won't ever be able to get any updates. If you are not sure you have outdated installers for everything, check first, because we don't have them available anymore.
I'm sorry, but you are submitting yourself to an entirely unnecessary troubles, just to continue to use an officially ( with "officially" I mean by Microsoft ) unsupported OS, when it could be so much easier to get rid of Vista, which is one of the most bugged version of Windows that was ever released.
And no, you don't have to upgrade any hardware. Any PC that can run Vista can run Windows 10 just as well.