见

见面 literally means see face, and it often acts like one phrase. In casual negatives like 我们几个月没有见了, people drop 面 because everyone knows you mean see each other. You can also say 我们几个月没有见面了; it sounds a bit fuller, not wrong. When you name the person, do not say 我见面他. Say 我见他 or 我跟他见面. Think of 见面 as having its object baked in, so a person cannot be bolted on right after it.

“我们几个月没有见了。” (We haven't seen each other for a few months.)

If something enters your view without much effort, 见 can fit. If you choose to point your eyes at something, use 看. That is why you 看电视, 看书, and 看医生, not 见电视, 见书, or 见医生. With people, 见朋友 usually means meet up with a friend. 看朋友 sounds more like visit a friend. 看见 is the special combo for successfully see, not a generic replacement for 看.

看 alone can mean look, watch, or read. It does not promise that anything registered. Add 见 and you get the result: your eyes caught it. So 我看了，但没看见 means I looked, but I did not see it. Use 看见 when the seeing actually happened, not just when your eyes were pointed in that direction.