1) If you are filming martial arts, you will want to have very good detail. A one chip camera is mostly an item for home movies. If you are going to be distributing this, look into a 3 chip camera.
When I say 'chip' I'm referring to the CCDs. The CCDs are chips in the camera that convert light into digital information. On a one chip camera there is one CCD that handles reds, blues and greens for every single frame 30 times per second. On a three chip camera the chips are devoted to one primary color, so each chip does 1/3 as much work, and the picture quality is crisper and the color is more true.
I use a Sony PDX 10, which is a great 3 chip camera that can be had for $2000 or less. It's also got an excellent shotgun mic and XLR inputs, if you plan on doing any audio recording.
2. Yes you can record direct to your internal HD with MiniDV, but it is not recommended. The issue is that you can lose frames when you are capturing to the same disk thaat you're booting off of. I suggest an external firewire drive. Make sure the drive is 7200 RPMs and has an 8 MB cache or larger. Make sure the enclosure uses the Oxford 911 chipset, or if you go FireWire 800, the Oxford 922 chipset.
You will be able to view the video in real time on your screen. Recording to tape is for when you've finished your project.
3. If you are going to be dealing with a lot of footage, I highly recommend FCP. The log and capture system on FCP is much better than that of iMovie and FCE in that it uses timecode from the tapes, meaning you can re-capture footage whenever you want, exactly the same way as before. You can also set up batch captures, where you pick all the parts of the tape you want to keep and then set the computer capturing it while you go outside and practice your kung fu. It's a huge timesaver. If you start by capturing in iMovie or FCE, you will not have this luxury, but you will still be able to use the footage in FCP (it will require rendering, though...i think).
4. FCE is basically FCP 3 with a lot of features taken away. FCP 4 is a very intuitive program once you have the basic idea of how it all works. I never took a class, but I did the tutorial included with the FCP 1.2 release, and that's all I needed. You can also go
here for some quick demonstration videos from Apple. If FCPs editing process is less cumbersome it is because it is less restrictive.
Hope that helps. Peace.