Give it spinach!
Can you solve this Mate in 16?
I'm still looking at your composition but meanwhile I want to point you to the "king walk" and similar "long checkmate" problems RewanDemontay posted on chess.com in the past 2 years. He too is a young aspiring composer who already has some length records to his name. His posts are worth studying as a measuring stick and as a generator of ideas for this type of composition!

Thanks! I remember looking at one @RewanDemontay composed a long time ago. I believe it was a selfmate named "Royal Circuit".
Considering the many king walk compositions out there, these two could be anticipated. I hope not
That's a valid question but also one you shouldn't worry too much about when you're young. I recall my first two endgame studies were anticipated - one turned out to be old theory, the other one was a "recent" (8 year old) production by a top composer. Actually, mine was a variation with different introductory play of the same quality. I was proud of that!

I found a cook in the second problem . White can put black in zugzwang and take the c3 pawn for a shorter route.
This should work, although I don't have an engine to try it out.
Usually cooks generate even better problems than originally intended but I haven't had the time to look at these diagrams yet. There is finally some good weather around here and I am biking as much as I can. I think though that your 1st problem is sound and I will give more comments on it. StockFish is still a good way to test short stretches in the solutions like the last 8 moves which are relevant to separate different candidate solutions. Be back later!

A dual in the new one - instead of Kh1-h2-h3, white can play a3-a4-a5 to but black in zugzwang. This should fix it
Here is the promised comment on the 16 move mate puzzle. Haven't looked at the other series of puzzles yet.
I think your 16 move puzzle is correct because I checked the last moves with engine help and used my own brain on top. The alternative plan Nh3-g1 (Pf3-f4) -f3 also works but requires the king walk as well and takes longer. Two relevant notes:
A. The king walk demonstrates crossing a river. The river is the 5th rank a5-e5 covered by the black rook. The crossing is very simple because you placed a dam on c5 which allows wK to cross on dry land. More interesting is to erect the dam during the solution as in the example below. However this version is not dualfree (more move orders) and needs to be reworked. The most famous river crossing problem I know is a retrograde made by Harry Goldsteen which he named "Charon". Charon was the ferryman who helped the souls of the dead to cross the river Styx in Greek mythology. Your river requires just one crossing and damming it off will do fine!
In the diagram below white must play the well timed move b4-b5 forcing a6xb5. Then the king crosses the river on b4 or a5. If white advances his pawn too soon then black will return the favor by pushing the pawn to b4 and the dam is gone! There are a number of things to figure out but I think the river crossing can be made to work! I didn't care about the number of moves in this version it's just the general plan!
B. The final moves and checkmate pattern in your solution are not that exciting. Much nicer are the mates after the moves Ng1, f4 and Nf3. That requires the white king to be near e8 as well so the king walk parts are almost the same. Currently your solution is faster but I suspect some tuning can be done to change that. For instance Nh3 could start on g1. But it probably depends as well on if and how you can solve the river crossing issue and what tempi remain for the black pawn. It's just a very interesting challenge.
I hope you don't feel I am overasking. These were simply the first thoughts I had about the position. Great if these goals prove achievable, no harm done when they can't. The composition job is all about getting to the max, not to the impossible.
Here is a puzzle I recently created. My chess engine (Popeye) broke
so there could be some flaws. Enjoy!
[Edit] King on g3 and bishop on g8 could work for a longer Mate in 17, but no Popeye means I can't try it out