I was wondering if I could custom build a camera that could shoot at least iPhone quality video, maybe with autofocus. Searching on Google doesn't yield anything useful about making anything. The only camera experience I have is my iPhone and Wikipedia. Is it possible and how would I go about doing it using currently manufactured parts?
If you want to hack something, probably the easiest way to do it is to buy a board-level system such as a Raspberry Pi and add a camera module. The Raspberry Pi camera module supports 1080p30, 720p60 and 640x480p90 video.
This will get you up and running quickly, and with the minimum of fuss. There is also an LCD touch-panel if you want one. The next step is to build your own housing - 3D printing, perhaps? Ready-made cases for the RPi are available - lots of them.
If you want to use your own lenses, you will need a bare sensor board with the right interface to connect to an RPi, and I don't know if any are available. You could possibly remove the lens from an RPi camera module. Obviously, you would have to make (or cannibalise) your own lens mountings. As for autofocus, I've no idea.
I've linked to the Pi Hut since their website gives a clear idea of what is available. The official Raspberry Pi site is confusing and looks as though it's designed to appeal to kids (which it probably is). There is also Raspberry Pi.SE. Raspberry PIs are also used for amateur astrophotography, so check some astronomy sites.