Cycling is what we call the growth of two specific kinds of bacteria that turn waste products in the tank from toxic ammonia to toxic nitrite and finally to nitrate, which is far less dangerous. Nitrate is removed by frequent partial water changes as it can be dangerous at high levels. It happens naturally as axoltols and uneaten food produce ammonia. The presence of bacteria food in the tank seems to eventually encourage their growth.
There is a nice article
here on cycling: how to do it and what it is about. If your tanks has been set up for two months or so and you haven't completely drained and scrubbed it (which I highly recommend against) you should have your beneficial bacteria and your tank is cycled.
I'll let someone else cover the sexing question besides pointing out
this page on axolotl biology which has information on sexing them.