Looks like your cycle is in full swing
Having plants in your tank will speed the cycle up slight as they produce ammonia like almost all organics. However, if your dosing ammonia (pure or in the form of food) then you really don't need living things in the tank.
I'll throw in my opinion with the light. The blue light should be fine, it tends to be quite dim and my axolotls aren't bothered by it. I wouldn't recommend the white light unless the tank is very poorly illuminated during the day, a display tank should always be clear enough to look good. Mine is very poorly illuminated so I use an LED strip on the lowest setting and it lights the tank up enough for the axolotls to be clearly seen without bothering them.
Just have a play around with it when you get the axolotl. If the axolotl shys away then its MUCH too bright. If they don't shy away but rarely wander and stick to the hides then it needs to go a little bit lower. Find a brightness that looks good and allows your axolotl to wander freely without being blinded.
The ammonia isn't the easiest to define between 0 and 0.25 so at this point nitrite is the clearest indicator of your cycle. When it shows a light cyan/blue colour it'll be clear that your cycle is over. Maybe it's because I'm colourblind, but I always have trouble see the difference between 0 and 0.25 ammonia and 40-160 nitrate.
Until then, crank the heat up to speed up the cycle.
