"Which platforms are going to do the targeting..."

These are called "ISR" (intelligence/surveillance/reconnaissance) platforms and among the forces afloat these could be the E-2C, SH-60B, "other aircraft," and drones.

"How long does it takes for weapons to arrive?"

Is mach 3.5 fast enough for you? https://en.wikipedia.org/wiki/RIM-174_Standard_ERAM

I mean, lots of nukes with 30 min travel time and 20-30 mile kill radius. Lots of new cruise missiles with mid flight trajectory correction. Dont need to hit a carrier if you can airburst a 1MT nuke 10 miles away to get a kill.

Have you heard of mutual assured destruction?

I mean, if we're talking about wars where adversaries have capabilities of attacking carriers, then those wars necessarily include nuclear weapons. The best we can hope is that those weapons are not used against too many cities.