My take:
The South hand is a 1NT opener for many.
As others have pointed out the auction only makes sense if 3C showed extras. The opponents should have explained this imho.
The 3C raise is interesting in another aspect in that it would usually show at least 4 in normal 2/1. It might be that they are playing a version of fred's method where balanced GF hands can start with 2NT. Again, if this were the case then some sort of explanation would have been in order.
I do not understand why North signed off after 5C - it seems blindingly obvious to ask about the
♣K at this point, either by a specific king ask or a specific suit ask. Once South shows
♥AKxxx and
♣AKx(x) North can count to 13.
Serious and Frivolous slam tries are different according to whether we are limited or partner is limited or we are both unlimited. You improve your slam accuracy notably if you can manage to limit one or both hands before reaching this point.
It is more common to play Serious 3NT than Frivolous. I would guess that Serious or natural would be the most common meaning for 3NT in such auctions depending upon the quality of the player you ask.
Slams almost always score well in low-level clubs, even obvious small slams where 7NT is laydown.
There are several possible auctions for my system here but this is the most probable. The structure over 2D is new so good practise to play with
.
1C = 15+ nat/bal or 18+ any
... - 1S = no 4 card major, GF
2D = 15-17 bal
... - 2S = puppet to 2NT
2N
... - 3C = 5 card major?
3H = 5 hearts
... - 3S = agrees hearts
3N = no spade control
... - 4C = club control?
4D = yes, but not diamonds
... - 4S = RKCB for hearts
5C = 0 or 3
... - 6C = club ask
6N = CK, no CQ
... - 7N