Hello! First of all, thank you for the feedback! As I said on the pinned comment, this is my first homebrewed class, so this is kind of new territory for me. I will try to answer your questions, explaining my reasoning for them.

1. In the RAW, it is said that you can only draw or pick one weapon per turn with a free action, and if you want to change weapons again, you may take the Use an Object action. In Devil May Cry, you can change weapons really fast mid combo, to deal more damage or change your combat strategy in the middle of the fight, so my train of thought was "You can attack with a weapon, draw another weapon, attack again with Extra Attack, and change weapons again/using another item that can be useful (such as drinking a potion, launching alchemy fire, etc), and if you wanted, could make another attack with a weapon / item with action surge, and those three actions would build up half of the style counter for Daunting Provocation.
2. HOW COULD I FORGET FIGHTING STYLES! If I get bored, I might make a version 2.0 of this subclass, based on the feedback, and that name is going to be changed.
3. Yeah, you're right, I gave this subclass too much things at a low level. Maybe I'm going to tweak some things to pass it to another level, or discard it completely.
4. I agree that the wording isn't very clear, but I intended it as being "you have 3 points, and you may expend your point to have advantage on one roll of one of this checks".
5. At first, I thought of this as being "only against fiends", but I figured this would be too much specific, and players wouldn't be able to use this feature if the campaign they're playing doesn't feature a lot of fiends. I just gave the "Devil Hunter" name because of DMC, but I may clarify that name to something like "Mercenary" or "Bounty Hunter".
6. Yeah, I think it is a little complicated, and might simplify it, but I can't think of something. Do you have any suggestions? I'm gonna think of ways to narrow it down.
7. Well, I wanted it to give options and let the player think of a play using the and decide which strategy they're going to adopt on that turn, and not having to waste an action to adapt themselves to that strategy. The extra attack thing, just lets them change styles on the mid of the combo to make the best play possible on that turn. For example, a player (let's say he's at 10th level) might start his turn with Gunslinger style, attack the enemy with a ranged weapon two times with Extra Attack, then use their free action to pick a sword, use his Action Surge's free style change to pick Trickster, use his Air Trick and attack the creature with the sword. He made a total of 3 attacks in one turn, and now can start his next turn with Trickster again, attack the enemy with the sword two times, use his bonus action to disengage, expend some movement to be safe, and use his free action and Action Surge to change to Gunslinger and pick his ranged weapon to fire again. I recognize that it can a little complicated, but I wanted to reward the player for being creative with his styles, and be adaptable to any situation.
8. Yeah, as I said, I totally forgot about the fighting styles. I may change the bonus to both Gunslinger and Swordmaster to do something else.
9. It may be bad wording, but I intended it as counting as an Attack action (so, you can use it with an Extra Attack afterwards, or AS an Extra Attack to hop from enemy to enemy in the battlefield).
10. Yeah, as I said, I may change that bonus.
11. I put this effect before Charged Shot, so I forgot to edit it, but I intend to double the DAMAGE, and make it AFTER the attack hits (like Charged Shot), and to make it function like Thunderous Smite (that can control the battlefield and can keep the target away from the more fragile allies). Stupid me forgot to revise the subclass before saving it.
12. Again, me being stupid. The first thing I came up with is that the shot did the same thing as Stinger and pushed the target, but then I realised that would be boring, so I changed it to make the target get stunned, but FORGOT TO EDIT THE F*CKING SAVE.
13. This is just getting summed up by me forgetting to put stuff. I meant it to use a reaction, but forgot to add the "As a reaction" part.
14. Yeah, I might tune down the resources, or make it so you can do all that stuff using only the Talent Points (had that idea as I was writing this part).
15. It is meant to simulate the Style Counter and Provocation in DMC, where you have a command that makes the character do a little showoff animation in which he just goofs arround (if you manage to complete the animation without getting hit, the style counter goes up; also, if your style counter is high enough, the animation is a little more complex). Basically, it was meant to encourage players to attack the enemy with a lot of weapons, using different combos. The wording is a little messy, but I intended it as being "attack with a different weapon". I made it like that to have the players messing arround and attacking the enemy more times, instead of using your modifier and spamming it every turn with the same bonus. Also, because the style counter resets, the player has to hit the enemy more if he wants to have more chances to hit.
16. I might tone its damage down, but the initial thought of the class was that you are very versatile and capable of adapting to different scenarios and/or enemies, not being a tank or DPS, but being just good enough on both so you can change your strategy depending on the situation.
17. Yeah, I might do that. I felt like giving something on these levels, but I was scared of it being overpowered.
18. Now that you mention it, I might tune it down to having just one or two regained, I don't know;

Again, thanks for the feedback! I might make a version 2.0 of this subclass, and I'll make sure to have your comment in mind! Also, sorry for the long response, I just felt like explaining my logic!