Going to way overanalyze #1. Everything is based purely on my memory (which is not entirely accurate) so I could have some embarrassingly bad calculations here.
Broadly, an argument for Link or Cloud would be that they missed 2005/2006, but the tournament of champions/bonus matches in both years + the sheer number of finals they've reached still keeps them in contention. Also not trivial is who made more matches between Link and Cloud. We know Link has a headstart because Cloud got eliminated in the quarterfinals in 2002, but because of Loser's bracket in 2018, Cloud should have an extra 2 (?) matches (Link faced Ganondorf, Pikachu, Cloud, Zelda, Cloud. Whereas Cloud faced Alucard, Crono, Link, Crono, Mario, Zelda, Link). Cloud should also have an extra match in 2003 when he eliminated Link in semis. In every other contest, they should have an equal number of matches since they beeline to the finals. Well, all except 2013 and I'm not sure who got eliminated first. I know Draven/Mewtwo/Sephiroth and Draven/Snake/Samus happened after Draven/Link/Shepard and I know Squirtle/Pikachu/Snake and Draven/Snake/Samus happened after Cloud/Squirtle/Leon(?). So it ultimately I think Cloud wins by 1?
The argument for Sephiroth is villains (32 villains so there should be 5 matches) Sephiroth also made the main 2018 bracket, but that's misleading because he should have 4 matches (Wesker, Ryu, Ammy, someone else) in the main bracket but only 2 (Tifa, Mario) in the legends bracket because he got eliminated early, so the total 2018 number should be 1 more than Link. I think Sephiroth made it to the semis in 2013 after beating Kirby and lasted longer than Link/Cloud so he might gain 1 there. This gives Sephiroth a lead of 7 so far and the question is whether how much Link beats him in the other contests. Sephiroth has the same number of matches as Link in 2002/2003 combined and has 1 fewer match in 2005, 1 fewer match in 2010 and 2 fewer in 2006. I really can't 100% remember exactly when Seph exited in 2004/2007/2008, so the rest is a bit of guesswork. I think he made the semis in 2004 (where he lost to Cloud) and he definitely wasn't in the finals for 2008 (It was Snake/Link/Cloud/Crono I think). The big wildcard is 2007 since I can't remember if it was Snake or Sephiroth who was in finals with L-Block/Link/Cloud. I feel like its Snake who snuck by with Cloud/Seph LFF, so I'm going with Cloud > Link = Sephiroth (with Cloud winning by 1 match)
Finally, the argument for Samus/Snake is that they actually made the 2005/2006 main bracket. 2005/2006 should have 64 entrants iirc, so there are 12 matches up for grabs total. Let's start with Samus. Iirc Samus made the finals both times (I think Mario vs Samus was the 2005 final but not 100% sure) but got eliminated first day in tournament of champions giving her 13 matches total in 2005/2006. She also made the finals in 2013, giving her a lead of 8 ahead of Link for 2005/2006/2013 combined. She should have 5 matches (Tifa, Mario, Tifa, Snake, Mario) in 2018, tied with Link and 2 fewer in 2010. Now, I can't remember exactly how well she did in 2002-2004, 2007-2008 but I don't think she even made the semis very many times if at all, so I think she's last place by a good amount.
Snake made the finals in 2006 and went 4 days in the tournament of champions. I honestly can't remember how he did in 2005, but he was weak. So I think he was in around 13-14 matches in 2005/2006 combined? He also made the finals in 2013, giving him a lead of 8-9 ahead of Link for 2005/2006/2013 combined. Snake also had 4 matches in 2018 (Zelda, Auron, Sonic, Samus), which is 1 fewer than Link and 1 fewer than Link in 2010, but I think he made the final in 2007 and for sure in 2008. Like with Samus, I can't remember exactly how well Snake did in 2002-2004 but he was weak, weak, weak so I still think Link edges him out, but he's probably ahead of Samus.
In the end (based on my probably horribly wrong calculations) I think Cloud might have the most matches surprisingly.
Cloud > Link/Sephiroth > Snake > Samus.
Feel free to correct me on any of these points, since I probably missed a lot of stuff.