Can you beat this shmup?! (Want feedbacks!)

I'm not a huge shmup fan (not since the DOS ones I played as a kid), but I gave it a try. I beat the first four levels.

-I was shocked that it didn't support my 360 gamepad.

-I was a bit disappointed that I didn't have any control over my shots. I know it doesn't really make a difference if I hold a button to shoot or have it auto-fire, but it made it feel like I wasn't in control and made success less satisfying.

-I really disliked how my bullets auto-aimed slightly. In level 4, against the two bosses, I ended up killing the one I wasn't aiming at before the one I was trying to take out first. It just feels like I'm cheating and, much like my previous point, it takes away some of the satisfaction of beating levels.

-I was disappointed to see enemies already being reused in the fourth level. I know their behaviors were different, but at least some different colors or something would be good. It felt like you'd already run out of enemy ideas (although I see from your GIF that there are other ones later).

-The difficulty curve is very strange. Stage 1 felt far more difficult than Stages 2-4.

-I found it strange that the "Level 2" button was so prominent. I kept almost clicking it by accident because my cursor was left hovering over it after the previous window.

-I found it a bit clunky getting into levels. It takes so many clicks. Have you considered removing the phoenix-selection screen? If people want to change, maybe they can just do that some other way rather than being asked every single time they go to start a level. I just wanted to move forward, but between the multiple windows and the buttons not being where I'd expect them to be, it took a while to get into each level. Ideally, I would like to be able to just click twice or something, with minimal mouse movement, and get back into the action.

-This might seem to go against my previous point, but I found it strange that after beating a stage I got automatically moved to the next. If I want to try the higher difficulty level, I have to click outside the window, move my character back and go through the whole process again. Maybe a "Go to Next Stage?" confirmation would be a good idea.

-The world map felt a bit too plain, I think. I realize that the land looks a lot like the land in-game, so that's not too bad. Maybe just adding some texture to the water would help. I also felt like I should be able to move the camera around, but maybe there's a reason I you want to restrict it so much.

-It wasn't clear to me if my reward for beating a stage was automatically applied (like +2 Damage or whatever it was), or if I had to manually do that somehow. It also wasn't clear if I had an opportunity to get a reward on any stage, or if some stages always only give stars.

-Apart from looking at the enemy health bars, I had no indication of how much damage I was doing. Some sort of visual feedback would be nice. It didn't even feel like I was doing anything at all, and then I'd see the boss die suddenly.

-I really like the music.

-The bosses I fought looked pretty decent and I liked their attacks. I also like that they change up their patterns fairly often, so even though I'm using the same weapon on and on the action doesn't get too stale.