I am not sure if they get "lonely", but I have always kept more than one just because I really like them
You could probably keep 2 in that tank, but I think 3 is too many.
Algae seems to always grows faster in my aquariums that have exposure to windows. The sun doesn't hit the tanks mind you. Axolotls do not like bright light and sunshine would heat the tank up (which you do not want), so a non sunny location is good.
Remember to cycle your tank before you buy an axolotl. Naturally cycling takes 30 days or more.
Buy a good test kit that will allow you to test for ammonia, nitrite and nitrate.
There are a lot of posts on cycling in the forums, and you can also google it if you need more info, or of course ask questions here.