First of all, don't take it personally.
I am not a quad copter builder of some sort myself, but your setup is flawed:
- Battery can deliver 30A constant, maxed out. Your motors take, at full power, 8×4 = 32A. You might get away with this battery, but it won't last long because you are pushing it too hard.
- Big, heavy battery, low power engines/esc/battery. I don't even think your copter is going to lift of with this setup. Engines of
only 80W on a quad that, taking a look at your picture, is going to
be relatively heavy, is asking for trouble.
- PDB is okay with this, and future, more power-hungry (I think), motors. They probably have a safety margin, but don't push it too
hard, which for now, you are not.
- Arduino: you are going to try and program it. Programming a quad isn't an easy task, and unless you are quite a skilled programmer, I
recommend you to buy a programmed board, something like this: Hobby
- I don't know a whole lot about copters, I'm more in the plane business, but unless you change motors, these props seem too big.
Moral of the story: get bigger engines, bigger battery, bigger ESC.
- I can try to recommend better motors, ESC, etc., but I won't. I don't know enough about quads to be certain it is going to work, and
I won't recommend you something I don't know for sure, sorry.
It costs to much for me, any way to keep the frame and change the parts to be cheaper and yet a good quadcopter?
First make sure that your setup is right, then start asking where you can get it cheaper, that's my advice.
Does the propeller fit the motor?
You are going to need an adaptor, but that is normal, I'd bet there are adaptors that suit your needs.
Any place to buy these for cheaper?
Yes, but you are missing a few (important) parts, the setup you present here isn't a very expensive one, if you can't afford it, I recommend you to save money until you can buy a proper setup, you won't regret having some patience.
Is it a good frame?
I can't judge if a frame is correct by one picture, there are way too many variables (like thickness of the material, where you are using aluminum, and where you are using the plastic, how are your motor mounts, what material, so on...).
Am I missing some parts?
Yes, since I think you want to control it, you are going to need a controller, add 25$. Materials for the frame, camera, transmitter for the camera, ground station to receive, monitor for the video feed, so on.
I think you are taking this too lightly. You don't just build a quad for the first time, it's going to take a lot, and I mean a lot, of trial and error, and quite a bit of money.
Take your time to find the right parts.