Shortly: With technological advancements, the S band radars that were only previously meant for early warning against air breathing targets will now be used also for guidance of anti air missiles. Furthermore there will only be a single x band radar against surface targets. The radars will be...
But it is an AESA radar so you can allocate a fixed or dynamic ratio of modules for scan vs illumination and have an overall larger multi purpose radar than have multiple small ones. The rest is programming.
I mean AN SPY 1 is also S band and Arleigh Burke doesn't have big X-band radar, neither does Istif or FREMM( S or C), or Type45( L and S band) so why can't we do it without X band primary radar?
You can strike strategic targets but a country with such a reactor will likely have sufficient defenses and nukes, and nuclear reactors won't explode like a bomb, more like chernobyl. And attack on nuclear facility will be considered nuclear war so they will be justified to strike you back.
Some of the things you need for a naval fighter:
Stronger body, larger and stronger landing gear, lower stall speed, higher stability at low speeds ( which probably requires reimagining the wings entirely, arrestor hook, some specialized avionics for ship approach, folding wings, corrosion...
