Supersonics like Oniks has been rated as low as 10 meters, so does the last Moskit. There are claims they even go down as much as 5 meters.
Any missile(or plane) can go 0.5m above the airfield. The problem is doing the same above actual sea.
Supersonics - especially air-breathing ones - will never catch up to subsonics in this aspect - and the faster they go, the more the difference. It's pretty much a hard limit.
I don't even know why you think plumes are a big issue as turbojets do produce enough of that. You cannot hide the plume enough because whatever you are going to add to a missile, will add weight and drag and reduce its range.
Almost all modern subsonics take measures to hide their plume; NSM - relatively less, LRASM - relatively more. Supersonics are in no competition here, because of hot air(ramjets especially so), and comparatively huge&uninterrupted flow of air. Speed doesn't come by itself.
p.s. on turbojets - it depends on the missile in question. There are small/low resource turbofans. Furthermore, small turbojets are exactly that - small.
For supersonics radar is necessary? All missiles do not need to emit radar until their final stage.
Yes.
(1)rule of thumb: all supersonic ASCMs use ARH. Quite a few subsonics are either mixed or fully passive - it depends on the concept of the missile in question.
(2)all missiles need to find target for their attack. Supersonics tend to do it earlier - because, obviously, (1)their speed and thus search has to be performed correspondingly earlier, and (2)they typically have no time to perform overly complex search patterns.
The missile is subject to flight corrections via datalink which will have to be done by satellite as a router, aircraft, UAVs, or even other ASMs.
Use of datalinks (external updates) actually plays against supersonics. Because if you have access to them - one of the big advantages(ability to shoot on unapdated target data due to far higher speed of the missile) actually goes down the drain. If you're investing in sufficient airspace control to provide these updates - you may very well both save money and make your attack sneakier by avoiding the sound barrier.
As for stealth, supersonics have a much angled nose, in addition to adjustable inlets that are also highly angled. So you can expect frontal (I mean frontal, not the sides) RCS to be low.
Your whole shock cone reflects, and you have a comparatively huge missile, which flies comparatively higher, and can't (aerodynamics!) hide its intakes the way subsonics can.
p.s. Kh-59 on your photo isn't even a true ASCM, more of a 1980s vintage multi-purpose stand-off precision weapon. Her modern relative looks like this:
You think the Chinese adopted supersonic missiles because they were inclined to adopting a Soviet doctrine? The history of Chinese antiship missiles have been by far and large, subsonic and they have no institutional overhang or momentum for bias to favor supersonic missiles. The missile they copied from the Soviet Union to produce the Seersucker and Silkworm missiles, is subsonic. Then came the era of Western European influence, particularly from the French that brought the C-801/YJ-81 from the Exocet. The Chinese was probably never convinced of supersonics themselves until they got a hold of the Moskit and saw what it can do, so they made a spiritual copy of it as the YJ-12 though they did have their own prototype supersonic ASM projects themselves, notably with the C101. The YJ-18 can be considered as mostly subsonic, the sprinter only works around 20 to 30km from a range total that can exceed 500km. If they are made to convince in the use of supersonics, even for a sprinter, it is because they have first hand, right at the front seat, experience of seeing it, testing it, collecting data for it themselves. It will be a decision made objectively and not through institutional bias.
This is an interesting part. For anything better than an educated guess, we'll have to go into chinese naval periodicals - and being blunt, I neither can read technical mandarin fast enough to do it now, nor do I have access to the translations (not a staff naval officer).
But given the choice of platforms - IMHO it points exactly to that.
YJ-12 is being employed from:
-H-6 family(main platform).
-Land launchers(defensive platform)
-Older destroyers(persistent at-sea platform).
While ideas of their employment may be different (and these forces are inherently flexible in their employment) - this is quite a typical "defensive" sea denial setup(defense through the threat of overwhelming salvo). In principle this mix, relying on mainland- and space-based targeting assets can reliably destroy just about any viable surface force within its reach, freeing modern force for other duties.
With this force at its current/future size(including units coming out from MLU) - I don't think there is need to arm frigates and corvettes with more heavy supersonic missiles. Their instrument is of far more tactical OtH nature, and their targets are far more diverse.