SCOTUS invalidated the core of the relevant law rendering it moot/unintelligible. It cannot stand as is; convention is that when part of a law is struck down the whole law is struck down unless otherwise specifically enacted with severance directives. The KY definition of “marriage” was eviscerated, leaving no definition of the word to act on.
Yes, SCOTUS very much has that power and exercises it often.
Not legitimately.
The Constitution confers no legislative or veto powers on the judiciary.
The only constitutional authority they possess is the authority to adjudicate individual cases that come before them, and that only within the confines of the Constitution and all constitutionally-valid laws. No more. No less.