1) Be neutral as second nature before attempting. This takes everyone different amounts of time.
2) You don't really need to be taught this. In fact, I recommend not taking a photography class but there are a few great books on Amazon about it, I cannot recommend all three of these enough, but if you had to get one get Martin Edge's book, "The Underwater Photographer."
Winning Images with Any Underwater Camera
3) Most cameras will also take video.
4) Yes, my housing for my a6000 takes a lot of maintenance to keep working correctly and protecting the camera/lens. The strobe takes maintenance too.
5) The tint is from a red filter. The red filter causes the camera's WB settings to compensate for the loss of red at depth. I hate filters and use lights.
6) I prefer photographs. Framing, lighting, exposure, timing... and you get details that I prefer over movement. If I had a decent stabilizing program I'd take more vids maybe.
I shoot a Sony a6000 in an Ikelite case using a manually slaved Sea and Sea strobe. It gives me RAW photos and does just about anything a DSLR will give me in a much smaller package. I shoot single strobe for the hard shadows and contrasts. I started with a GoPro but it sucked at photos. Then I upped my game to a little Canon point-and-shoot in an Ikelite case that had a diffuser card for the flash. It would have served me just fine for a long, LONG time but RAW is really necessary for effective post.
If i were you, i'd buy the Canon Mk IV package the other guy linked you. It an excellent camera and package with excellent lights for photos. I dont know anything about video lights, sorry. Buy these 2 books and start reading.
As for the gels/filters, read this blog post: https://www.waterdogphotographyblog.com/five-tools-for-creative-shooting-on-shipwrecks/
I'm using a Canon S110 in an inexpensive Ikelite housing along with a Sea&Sea YS-D1 strobe as a step before getting a housing for my Olympus E-M1. You can see some of my photos here.
With a compact camera (make sure it can do RAW) + an inexpensive housing you can get nice shots and if you add strobes those can be transferred over to a nicer camera later on when you upgrade.
Also, if you want to do some reading, I really like Martin Edge's "The Underwater Photographer".