Okay, so, the reason your water is cloudy is probably because of the vinegar. You need to actually rinse it out with running water, not just let it dry up because it's still there. You should empty the tank and refill it.
Now, as for your parameters, the reason they are testing well is because, well, you probably killed the cycle. I could be wrong about this, but at least from what you mentioned, it sounds as if you don't have a source of ammonia. Ammonia is bad for your future axolotl, but ammonia is the "food" for the bacteria that make your water safe. Aquatic creatures and decaying matter produce ammonia, which is eaten by bacteria that then produce nitrites. Nitrites, in turn, are eaten by bacteria that produce nitrates. Nitrates are eaten by plants or removed through water changes. If you don't have a source of ammonia, the whole chain of bacteria starves and dies. You will likely need to restart your cycle (again, unless I'm wrong about your lack of ammonia).
Also, I too have issues with internal limescale marks because of how hard the water in my area is. You can somewhat prevent them by topping off your tank with distilled water (don't use your normal water, because this just adds more minerals; you want to replace the pure water content that has evaporated). I also use a new razor blade to occasionally scrape it off the glass. It works great and is very satisfying!!
Last note, you don't necessarily need a lid; leaving it off can be a great way to cool your water through evaporation. If you're worried about your axolotl jumping out, you could use a screen lid and get the best of both worlds.