Question/Comment: "blurry and unfocused images?"
Answer: Then you should focus your lens (you may even need to do it manually) and not shake the camera when you take a picture (make sure you are using a fast enough shutter speed)
Q/C: "anytime I attempt to use sport mode, it does not function properly and it is difficult to catch moving objects. why is this?"
A: Because you are misunderstanding the function of sport mode (it uses the fastest shutter speed available under existing light conditions. If you want continuous focus (called "servo") then set your focusing to servo mode. If you had just taken the time to read your manual you would know this.
be aware that servo mode is not perfect (no camera can perform miracles - otherwise everyone would be a professional photographer)
Q/C: "when I use my 75-300 mm lens, the quality of the animals I shoot is downgraded."
A: I believe you mean 'degraded'. That's because that lens is not a high quality lens. don't get me wrong, that doesn't mean it can't take good pics (it can, because I have that lens), but it's not as sharp, especially at the higher end of the zoom (300mm). I get better luck with manual focus when I use that lens.
Q/C: "I do realize that I was not using a tripod, but I had a steady hand and I propped the camera on something to hold still."
A: You may think you have a steady hand, but the camera may not. And the proof is in the pudding.
Q/C: "I tried many modes but it was always a good shot but unfocused or really grainy and bad coloring."
A: If your camera is having trouble focusing automatically, then that's what manual focus is for. Grainy has to do with not enough light (or too high an iso setting). Bad coloring might have to do with the automatic white balance setting (that's what manual white balance is for).
Q/C: "I have had this camera for 2 years and have lost my interest in photography because of these problems"
A: well don't blame the camera for that. people (non-professional) have been enjoying photography for decades, with less advanced cameras. Today's cameras make it so much easier. If people from 50 years ago can get enjoyment from their primitive cameras and you can't from your more advanced camera, then maybe you are barking up the wrong tree.
Q/C: "unfocused pictures/images"
A: Do you mean blurry or out of focus? Those are two entirely different issues. You may wish to clarify.
Q/C: "I have bad vision though (not horrible, but difficult to see when I am photographing) which prevents me from doing much on manual mode."
A: Not to be rude but that's a load of crap. I'm nearsighted and I am able to manually focus as long as I have glasses or I adjust the diopter on the eyepiece (assuming yours has one).
Manual mode has nothing to do with manually focusing a lens (if you had read your camera manual you would know that).
Q/C: "Should I invest in some universal lenses that are NOT kit lenses or possibly a flash? Which might be better?"
A: You should invest in a good book on picture-taking. That would do a lot more for improving the quality of your photos than a new lens or flash (at this point, considering all the trouble you are having, I would actually not recommend getting an external flash. Flash photography is not easy to do well, even for experienced photo enthusiasts).
Q/C: "seriously, every time I ask for advice, you people get ruder each time."
A: Relax. Some people are just trying to help. The truth can hurt sometimes.
Q/C: "NO, I CANT read a manual because I'm the kind of person that has to learn by DOING, not READING. Not everyone can do it your way, sorry."
A: Talk about rude (not to mention stubborn). You won't learn with that kind of attitude. People learn BOTH ways, by reading AND doing - capische?
I'm a visual person, but I learned about photography all on my own by reading and practicing. READING and putting the concepts I read into practice. I did this without the internet. I even did this without a manual (I had to go and buy a magic lantern guide for my camera because I bought it used. Years later I found a manual for my camera and keep it as a reference). I went out and learned what I could. I did not whine about my eyesight or my propensity for learning by doing - I just applied myself.
trial and error (mostly error)