First one is definitely an FFC, it seems counterintuitive to have self-capture and giveaway, but the bare piece rule gives an extreme level of strategy. There may be a better starting position (perhaps with more pieces, to dull any large starting advantages one side may have), and it is very similar to Solo Chess, something that is extremely unique among variants. This could work well as a WoF (speaking of which, are WoF arenas going to resume? I remember 2-3 of them right after the merge, but then they disappeared entirely)
The second position would probably fall under Standard Position, but it could also be an ADC. It's so similar to normal chess that it doesn't seem worth consideration.
Also, I would personally recommend removing unnecessary gamerules, such as Torpedo & En Passant (do not affect gameplay as there aren't really any scenarios where pawns would be pushed 2 squares since it is giveaway, and Deadwall because it is a 2 player variant meaning once a player is dead the game is over,
two position classifications
If you see my other topic I have four potential WoF templates and I have submitted one currently, I don't know the status of WoF though.
The level of strategy here on the giveaway template may allow for some unique starting positions yes. The torpedo is an intentional choice as at least for my strategy I will move my knight on the first two to three moves to capture my other pieces, leaving the knights alive usually unless captured. Doing so allows for a later game when you intend to destroy key enemy pieces early like the rooks and queen, and after such a position is reached they have little but pawn moves left and to compensate the extra moves are allowed. The stonewall is purely aesthetic as when they lose they turn to stone, easier to see who won definitively.
I mainly mention the giveaway template, it may be interesting as is or modified considering the possible FFC status. But the second template I have considered to change the starting position or include some extra pieces to make it more interesting.
Such as pre-pushing the pawns. I like an exaggerated grob or borg (with an extra push of the pawn) personally as a way to attempt to deny movement of enemy knights forwards, however this strategy has many drawbacks generally, a forwards positioning of the pawns somewhat achieves this goal while allowing some side strategies to surface. For example:
(alt) F4 pawn takes G5 on move 1 suffices as a stand-in for the strategy I described, but other strategies or positions may be viable here. As note, extra pieces may be put in the extra empty spaces between the pawns and the regular pieces (or other pieces swapped in place of the regular ones), for this setup I preferred to place them only upon the B/C and F/G squares on the 2nd rank for white and vice-versa.
https://www.chess.com/variants/custom/game/27086113/1/3
https://www.chess.com/variants/custom/game/27091108/1/3
Here are two positions I made before some of the recent updates, I am wondering what they would be classified as and if they might be good as a ncp/wof.
https://www.chess.com/clubs/forum/view/classification-of-concepts
The first one is interesting as I think it will be a Fundamentally Flawed Concepts (FFCs) specifically because it is a "Concepts that purposefully break the rules of common sense" and yet when playing there can be a lot of strategy to this simple giveaway template.
The second one is a lot like classic chess except that draws are pretty much out of the question, and you promote to a knight rider instead of a queen. I think this would be a standard concept.