Ok if you get stones make sure they are too big to fit in an axolotl's mouth.
How big are your water changes each day? Don't do more than 20% as too big a change in the water will stress an axolotl. Also, do you have a filter and is your tank cycled? If you don't have a filter you will need to do water changes more frequently. Also, when your tank was set up a few months before your axolotl was put in, did you cycle it? I was asking as you say you don't have an ammonia test kit so perhaps you did not look at the parameters? Read this if you are unsure about cycling->
http://www.caudata.org/cc/articles/cyclingEDK.shtml
Generally, axolotls are best left without other tank companions like snails. Snails breed really fast and also if they large they can damage your axolotl. But many people have snails without any hassles so it depends on how you manage them. If you buy snails from an aquarium you probably should quarantine them before putting them in a tank I think...
Anyway I think you should get ammonia, nitrate and nitrite tests ASAP to make sure the water quality is ok. If there is ammonia present you will need to do daily water changes of 20% until it is 0. Any ammonia is harmful to your axolotl. Also to help keep ammonia under control you should do spot cleans of any axie waste or uneaten food.
Finally, get a thermometer to measure the temperature in your tank. Ideally it should be under 20C. Anything above 24C will be really stressful and most likely your axie will die if exposed to that for a day or so. You *can* keep your axolotl in the fridge. Just make sure the temperature in the fridge is above 5C (you can put a thermometer in a cup of water near the axie container to keep an eye on it). Then with the container your axie is in, cover it with a tea towel or something like that to block out the light. At fridge temperatures axolotls often stop eating so don't worry about that. Finally, in the fridge you must do 100% daily water changes to stop any ammonia building up. I keep a bottle of dechlorinated water handy in the fridge to do the changes.
Anyway, good luck with your axolotl, she is cute