Not sure why I keep concerning myself, but…

[ElvisLives]

The likelihood of ever seeing one is infinitesimal, but, we’ll still be expected to know everything about a Fair Catch Kick. I heard from an unofficial, but reliable, source that the game clock will start on the kick for a Fair Catch Kick. That makes total sense, if everything (well, most everything) after the kick is to be treated like a scrimmage kick.
So, if that is the case, then having an onside kick would be non-sensical (B could just let the ball go OB or come to a stop, and have good field position at the previous spot).
I’m guessing:
-If unsuccessful and untouched by B, B gets the ball at the previous spot.
-Fair Catch made in B’s end zone, will be a true touchback (stupid move by B).
-Team A would not be allowed to touch the ball until it is touched by B.
-After a fair catch by B in the field of play, the ball would belong to B at that spot (even if behind B’s 25).
-The kicker would not be able to be blocked until he has advanced at least 5-yards beyond A’s restraining line or the ball has been touched by a B player, or has touched the ground after being kicked.

Let’s see how far off I am.

[Legacy Zebra]

An onside kick wouldn’t make sense anyway, since A could have just snapped the ball after the fair catch anyway. Team A already has the ball. Why would they give B a chance to take it away? As far as everything else, I’m not sure why they’re mixing free kick and scrimmage kick rules for this. All they had to do was say “All free kick rules apply. Exception: if the kick passes through the goal in flight, Team A scores 3 points.” They’re making this way more complicated than it needs to be.

[ncwingman]

All of this got me digging a bit more into the existing rules - that you've probably already done yourself. The NCAA's statement on the rule change said they wanted to essentially have the same rule as the other codes.

The Fed rule, as you've been asking about elsewhere, is essentially a free kick that can score. Formation, timing, clock status, first touching, etc... all of that is "free kick" standard.

The NFL, on the other hand, treats it as a scrimmage kick with an odd formation, and all scrimmage kick regulations, timing, clock status, etc. apply. (11-4-3: "The rules for a field goal attempt from scrimmage apply to a field goal attempt following a fair catch (a fair catch kick).")

From what you've said so far, it sounds like the NCAA is copying the NFL rule over the Fed rule, so I would probably default to "Is this what would happen on a field goal?" as my thought process. Of course, they'll also change like three things randomly just to be difficult.

Edit - To add the rest of the NFL rule, that explicitly states that A cannot possess the ball until it has been touched by B, therefore an onside kick would be nonsensical.

[ElvisLives]

And the first one of us that has a Fair Catch Kick, get video and upload a link to it. Taking bets on how long it will take to see one. 

[Etref]

And the first one of us that has a Fair Catch Kick, get video and upload a link to it. Taking bets on how long it will take to see one. 
[/quote

Just because you said it…… will happen Week 1 noon game!

[TxJim]

So, thinking it would have to be a Valid fair catch signal given as well, (no other invalid signals given by any other player included) since the rule defines a catch after an invalid signal is not a fair catch.
And will, by interpretation, a valid fair catch signal given but the receiver was illegally contacted before an unimpeded opportunity to catch the kick (KCI) allow this kick?

[Ralph Damren]

I had a veteran coach ask me once if a player was stupid enough to call for a fair catch at HIS 1 yard liner, could he than free kick from there in lieu of running 3 plays and then punting from his own end zone . You may have some coaches at the NCAA level that may think 'outside the box' on this. TxJim is reminding us of the NFL FK=FG that us made last year after such a KCI call

[peterparsons]

So, thinking it would have to be a Valid fair catch signal given as well, (no other invalid signals given by any other player included) since the rule defines a catch after an invalid signal is not a fair catch.
And will, by interpretation, a valid fair catch signal given but the receiver was illegally contacted before an unimpeded opportunity to catch the kick (KCI) allow this kick?

NFL rules (which I also work in Europe) allow a Fair Catch Kick after an awarded fair catch (which is given if the receiver is fouled) as well as an actual completed fair catch. I'd guess that the NCAA implementation will be similar (even if the wording is different). I don't know if NFHS is any different to NFL as that's the one rule set I don't have to worry about.

In the NFL, a Fair Catch Kick is a field goal attempt from an onside kick formation (so either a held place kick or a drop kick, no tee allowed). Scrimmage kick rules apply.

I have seen one live. There was an unsuccessful attempt in the 2019 game in London between the Panthers and the Bucs at the end of the first half.

[Ralph Damren]

We New Englanders well remember the huge comeback in the Super bowl vs the Falcons to win in OT. With only seconds remaining in regulation ,the Pats made a FC at their own 39 . It was later mentioned that they could have FKed for a 71 yard field goal BUT IF MISSED the Falcons would take possession at the spot of the missed kick. Coach B musta' thought that thru  .

[Ralph Damren]

.....On a second thought, treating FC/FK as a scrimmage kick, wouldn't a missed one bring the ball back to the previous spot - like a missed FG from a scrimmage down