What causes the "sliming" in the water and can you get rid of it?

Your Sim can get the slimed moodlet if they swim through the green algae floating around, sometimes in what looks like 'clear' water too. I don't think there's any way other than bringing Mua Pel'am back into pristine condition to get rid of them. If you have a Sim in a higher level of the Conservationist career, they can survey the slime and perhaps get an option to 'spray invasive species.' The slim/algae will go away, but it seems to be temporary. I've had my Conservationist spray it and it was back the next day.

The glowing blue water is bioluminescence which only happens when the ocean is healthy or getting healthier at least. It usually doesn't appear unless your Sim has passed the first stage in cleaning up the island. I've never had a Sim get chills from swimming in it though, but she has swam through pockets of cold water and got chilled. Perhaps the cold pocket your Sim swam through just happened to be under the bioluminescence? I have no idea.

The only time I've had a problem cleaning up the yellow sulfur puddles from the volcano is when I had more than one in the queue for my Sim to extinguish. If you do just one at a time, they should go away. Removing those puddles will give your Sim 'points' toward cleaning up Mua Pel'am, so it's a good thing to do if you want to do that. It gives more points than just cleaning up the trash piles too. Check out Carl's Sims 4 website for more information. He has a lot of great videos and tips & tricks for all the packs.