For a super duper quick answer to your question:
I recommend the Panasonic LX3 or Canon G10 as the current best available point and shoot cameras for your purposes. I also recommend buying a tripod no matter what camera you use. You should probably buy the tripod first and use it with your current camera, since it really isn't half bad. I think once you figure you how to really harness its power, you may not be so swift to want a new camera in the first place.
Part 1 to the long answer (I'll wait for some feedback before I decide what entails part 2):
Tripod mounts are universal. If you buy a decent tripod, it should work just as well with any future camera you may purchase as it will with your current camera. As ironic and puzzling as this sounds, reef tanks aren't very bright subjects in photography terms. You are shooting a 1/10 of a second or even slower in some cases. The fact that the images above look as good as they do without a tripod deserves a round of applause. Surley you using some creative tactic to brace yourself as you took the photos above other than holding really, really still. My point is, if you buy a tripod and a tripod only, the results it produces with your current camera may surprise you.
If you plan to take a digital photography class, I can all but guarantee half of your time will be spent learning to use Photoshop. While many project images will be supplied by the instructor to standardize the lesson, I am sure you will be using your own photographs as well. The single greatest advantage digital trumps over film photography is image editing. To take full advantage of the greatest advantage digital has to offer, your camera needs a certain trait; The ability to shoot RAW.
RAW hasn't been standardized yet, and makes up Canon (.CR2), Nikon (.NEF), and all of the other manufactures versions. Think of a RAW file as just that...raw. Like a steak. It hasn't been washed of blood, marinated, cooked, seasoned with salt and pepper, or supplemented by a baked potato and ceaser salad yet. It is simply and beautifully a RAW virgin piece of steak.
The common "quality adjustments" on a camera tend to consist of: JPEG, TIFF, and RAW. Since your camera can only shoot JPEG, it probably has 10 different types of JPEG...but they really just aren't that importiant. You are trying to make art, so you want the highest quality setting every time. Simple.
When your Finepix E510 takes a picture, it immediately edits it. The camera decides how blue the picture should be, how to saturate the colors, how much extra sharpening to add, and a whole slew of other questions which need answers. After the image is edited, all of the RAW information is thrown away to make room for more images.
A RAW image is a raw steak that you clean, cook, and serve yourself.
A JPEG image is a steak whos fate you leave to the cook in a restaurant. It still tastes pretty good most of the time, but if you are a chef yourself...you could probably have done a better job.
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One thing that really does impress me with your little Fujifilm Finepix E510 are manual controls. I didn't say great manual controls, but you can actually work with it!
Remember Aperture, Shutter Speed, and ISO that I mentioned earlier? You can actually select what you want them to be!

Hurray! A photography class field trip sure would be boring if you were the only one who couldn't pick your shutter speed. I know because this poor kid in my own photography class just sort of kept his fully automated camera in his pocket and asked everyone else questions about their DSLRs.
When you take a picture, you have to be conscious about how bright the picture is going to be. I can take a picture at 3:00 in the morning of a house with the moonlight and make it look rather bright. I can take a picture of the sun, looking directly at it, and make it look a soft orange. I can take a picture of snow and make it look grey or pure white. Its all up to the man behind the lens.
The first thing you need to understand about photograph is metering. A sensor in your camera will look at what you are taking a picture of and tell you how bright it thinks the picture should be. Over half the time I would say this sensor is wrong, but if you can predict why it is wrong and how wrong it is, it becomes a very valuable creative tool.
Usually if you are taking a picture of something very bright (snow), the camera will try to make the picture too dark. You need to tell the camera to make it brighter than it thinks the picture actually should be.
If you take a picture of something dark (a black car), the camera will make the picture look too bright. You need to tell the camera to make it darker.
Eventually you will learn when the camera is going to do what, and make adjustments accordingly before you even take the first picture. If you are taking a picture of a tree for instance, Bryan Peterson's popular book says to make the picture -2/3 darker.
-2/3 what you ask? A stop. Everything is measured into stops.
ISO: 400, 200, 100 (doubles)
Shutter Speed: 1 second, 1/2 of a second, 1/4, 1/8, 1/15, 1/30, ect (doubles)
Apertuer: f/2.8, f/4, f/5.6, f/8, f/11, ect. (each multiplied by square root of 2)
ISO is how sensitive your camera is to light.
If the light hitting the sensor has twice the potency, the image will be 1 stop brighter. The higher your ISO (yours goes from 100 to 400, mine goes from 100 to 3200), the higher the interference. Just like turning your TV to a channel that doesn't exist, the side effect of high ISO are black and white and/or colored dots all over your image. These are two separate types of noise.
Shutter speed measures how long you actually take the picture.
If the digital sensor is left exposed for twice the time, the picture will become 1 stop brighter. If your shutter speed is 1 second, and movement taking place in that second will be a blur. Your pictures were taken at about 1/10 of a second. Most of us use a tripod for 1/100 or slower. 1/10 is a lot slower!
Apertuer measures how big around your lens actually is.
If the lens doubles it's width, it will let in 1 extra stop of light. f/2.8 is wider than f/5.6.
You can pick your ISO, Aperture, and Shutter Speed yourself. This is very empowering!!