Cherry Blossom

[lwd]

Let me rephrase what problems would the Japanese face if they attempted to store and launch a Cherry Blossom from an Aircraft Carrier?

Well looking at the page you mentioned above, ie:
http://j-aircraft.org/xplanes/hikoki_files/kikka.html
lets see there's this:

A take-off run of 1,150ft. when equipped with two 992lb. thrust RATOG bottles

That would be cut by a bit on a CV due to the CV speed but using up a ton of expendables with every take off is not an inconsiderable drain on resources.

Range of at least 127 st. miles with a 1,102lb. bomb load or 173 st. miles with a 551lb. bomb load

Without any bombs you could get a bit more range but this is till pretty short for a carrier fighter.

I didn't see what the stall speed was but the Me-262 had a pretty high one and a fairly long landing run off as I recall. The shock of landings may have been a problem as well the lever arm of the engines out on the wings like that.

[RF]

Could the plane, at least in theory, be launched by catapault?

[lwd]

If the plane wasn't designed for that from the first the wracking especially on the engines from both the catipults and the landings might induce structural failures. I'm not sure if you can use a catapult and the rocket assisted take offs at the same time. If not the catapult only buys you a lower logistics burden.

[Bgile]

If you look at a modern F/A-18 next to any version of the F-15, what immediately strikes you is the big difference in size of the landing gear. You notice the struts right away, but the whole assembly is much bigger on the F/A-18. That is what it takes to land on a carrier. Also, all of the early carrier based aircraft were tail draggers.