You're not supposed to remove the earwax that lines the deep insides of your ear... Its a natural secretion that protects your ear from infection. At most, just take a q-tip and clean around the outside of your ear, but definitely don't shove it down your ear, because then you're just shoving more wax down into your ear canal and making it more clogged + more prone to infection.
Most people will find it gross, but I just use my pinky finger and just scrape around the outside of my ear canal to get out the earwax that has naturally been pushed out.
Yes, except if you have excess earwax production. I have quite a bit of wax, though not to the point that my earcanal would get clogged (my coworker has this problem, he is almost always deaf in the left ear because his earcanal is clogged by wax), but I have to clean my ears frequently. In shower I use my fingers to clean my ears and enter of the earcanal, and fill my ear with warm water to keep my earwax wet enough so it would come out eventually in natural ways.