1 - close/nearby.

Both express lack of physical distance.

They can be used as adjectivally and have the same meaning in sentences like this: "The post office is close," or "The post office is nearby". We can also use "nearby" attributively with the same meaning; for example, "He comes from a nearby village."

"Close" can also be used figuratively to mean lack of emotional distance; for example, "a close friend". ("A nearby friend" - if it means anything at all - would mean "a friend who is standing a short distance away from me".)

To express the same thing by using them as prepositions, we have to say "close to" or "near". For example, "She lives close to me," or "She lives near me." Again, "close to" can have the figurative meaning of a lack of emotional distance as in, "I don't really get on with my mother, but I am very close to my father."

2- look/see.

These two verbs are not the same. There is, roughly, the same difference between them as there is between "listen to" and "hear". "Look at" is an intentional action - in other words, you choose to do it - meaning "I focused my field of vision on x", while "see" is, generally speaking, an unintentional action meaning "x entered my field of vision". (Although, this does not apply in sentences like, "I saw a great film last night.")

You could think of the difference like this: imagine your eyes are a video camera. We use "look at" for what you are pointing your video camera at, and "see" - generally - for things that enter the viewfinder. For example, "While I was looking at the sky, I saw a shooting star."

3 - back/ago.

I am guessing that you are thinking of phrases such as "many years back"/"many years ago". "Ago" is far more common in this context, especially in written English. In British English, at least, to use "back" in a sentence like this seems much more informal and colloquial.