All of the advice you have received so far is spot on. A couple places to start are to make sure you have your buoyancy dialed in and then to consider the weight of your system underwater. I generally don't carry my camera the first dive on a trip as I like to make sure I have my act together from a weighting and breathing system first before adding the task loading associate with a camera. You can either keep your weight the same and account for it with your BC or drop some lead. I prefer to drop some lead. I have a larger system (5dMk4) and have to take into account whether I have a macro port or big dome on it. You can use float sticks and other means to increase the buoyancy of your rig if you need to. Making your system lighter is really helpful for macro.
The next rule is to get close, real close, to your subject. Of course you don't want to be finning or hitting coral so you need to look for areas that allow access without damaging the reef that have something interesting to shoot. A great way to do this is to start your dive at the bottom of the reef (if that is the kind of place your are) and to really slowly work your way up. Then your body and fins are away from the reef. Find a piece of bottom that is not live coral to rest a finger on to stabilize yourself while you wait for the fish to get used to you. I was taught this trick by a photo pro on Bonaire and it really helps you get much more immersed in the fish life so you can get close shots and more natural behavior.
The final rule of thumb is to shoot level or preferably, up. Shots down are typically not very interesting and don't allow you to get much context into the background. Working your way up the reef really helps you see the upward shot opportunities. That said, some subjects are nearly impossible to get ascending shots of and you have to take what you can get. No picture is worth damaging the reef.
I think your camera shoots RAW and definitely take advantage of it. I use Lightroom from Adobe to edit them. You will be amazed what you can do with it to turn an iffy picture into a keeper.
I generally begin a dive with my camera set for what I think I am going to need. Usually in the tropics that is around ISO 100, shutter 1/200th and aperture of F8. The aperture will be smaller (higher number) for macro and larger (smaller number for wide angle.
Here is some of my stuff. I'm not a pro, just an avid hobbyist.