I am not sure I understand the question correctly.. or rather, every question in the Poll/OP seems to ask different things.
What are "fundamental mechanics"?
The way I understand the question in the Poll is "Which character requires you to understand how SG as a game works the most, rather than char specific knowledge"; eg "Valentine requires the most knowledge about when and where to call assists, how to avoid the opponents assist with your given movement abilities, how to counterpoke while spacing properly with good-hitboxes-but-slow-startup normals, etc"; "Filia requires the best bait/whiff-punishing fundamentals, as her normals tend to lose against stuff but she is too fast to be reacted to, so she has to pick her spots, see the opponent whiff a cLP AA attempt and use that tiny timeframe to go in hard"
This would eg mean Headless Fortune can't be voted for - while she is difficult to play properly, all her difficulty stems from head control, which no other character has and thus can't be called a 'fundamental mechanic' whatsoever
"Or otherwise has their tools increased by player knowledge" on the other hand would make Headless Fortune a very strong contender, as she is a bottomless pit of pressure, mixups, safety nets and zoning - her tool -namely the head control- gets immensely stronger for a long long long time while you learn her; but again, I don't see what a hyper char specific skill has to do with fundamentals.
"Which character requires the player to use them effectively in only a few situations" then looks to me like an inverse question - asking for the polar opposite of what was requested before (a character which only requires me to use them effectively in a few situations = a character which works well even if I just do random stuff in the majority of situations = a really easy character)?!
"Which character has tools only applicable for certain situations that the player needs to discover" then is again an entirely different question, asking for who has the most prominent niche tools; but this doesn't really tell anything?
You could say "Okay, Bella Horns is a niche tool that is only really applicable in a few specific situations" and it would be right, but that sort-of omits her also having access to Dynamo (.. and 50 other reversal options), which just beats everything clean - and as such, overall reversaling with her isn't exactly a difficult task
"Who's the hardest to get up and play with kek" .. you crossed this out, but again this is a very different question to the ones before. A character can have a really low skill floor while also sporting a high skill ceiling; the two aren't mutually exclusive
I can't really answer this, as I have no idea what you are actually asking about.
- "Who is the hardest character to pick up"
- "Who is the hardest character to get to a proficient level with"
- "Who is the hardest character to learn everything about"
- "Who is the character that relies the most on fg(/sg) fundamentals rather than char specific knowledge"
- "Who is the character with the largest amount of differing tools that have to be used in varying situations" (eg sporting 5 different air-to-airs rather than a single Fukua jLP)
Or something else?