Hi Kawaii. Extra slime coat causes the skin to look dull and gray, sometimes in patches and sometimes all over. It can also come off the body in whispy tendrils that look like fungus but aren't. If he had this problem, he would probably also be showing other symptoms like clamped fins.
The film on the water is a protein oil film that happens when the water doesn't get enough circulation. Feeding lots of high protein foods can cause this. I get them in any unfiltered tank and it's harmless but annoying. You can lay a paper towel flat on the water surface and it will soak the oil slick up. But the only way to really prevent them is to increase surface water circulation, usually by adding an airstone or sponge filter.