Learn English – My friend had left school ___ the age of 14 and gone to work ___ a restro

The following illustrates the meaning of these phrases in terms of set notation. A more grammatical explanation is covered here: https://english.stackexchange.com/questions/45371/why-do-we-say-of-mine-of-his-instead-of-of-me-of-him

We are friends of him. (Wrong)

We are friends of his. This grammar is ok.

The focus is on who "we are", where there may be other friends that he has as well. Here's an explanation using some set notation:

• We = {John, Joe, Jane}
  Him = Frank
  Frank's Friends = {John, Joe, Jane, Mary, Sue, Mark}
  {John, Joe, Jane} is a subset of {John, Joe, Jane, Mary, Sue, Mark}
  We are a subset of His Friends.
  We are friends of his.

An alternate form of the same sentence is, "We are his friends." This is a more natural sounding sentence, connoting a closer, more familiar relationship.

The reverse, "He is a friend of ours" focuses on "who he is" and has an opposite "ownership" sense:

• We = {John, Joe, Jane}
  Frank is one of John's Friends.
  Frank is one of Joe's Friends.
  Frank is one of Jane's Friends.
  Frank is a subset of "Our Common Set Of friends."
  He is a friend of ours.

Again, the alternate form, "He is our friend." connotes a closer, more familiar relationship.

^{Compare with "Those are cars of his." That means those cars belong to him, but implies he has other cars. However, the sentence "Those are his cars" can imply "Those are (all of) his cars." The difference is based in the common understanding of the world. We know that a person usually has many friends but a limited number of cars.}

We are friends with him. This grammar is ok.

The focus is on the relationship, which is mutual. The reverse, "He is friends with us" has a very similar meaning grammatically, but is not used as much.

• We = {John, Joe, Jane}
  He = Frank
  IsFriends(We, He) = True
  We are friends with him.

Note that "We are friends with him" is not as strong as "We are his friends."

We are friends. This grammar is ok.

In this case, there is a speaker indicating mutual friendship among a group of two or more people, including the speaker. It is the short form of "We are all friends with each other."

He's a good friend. This is another form that can be used when "we" or "I" is understood in context:

• "Do you know Joe?"
• "Yes, he's a good friend" = "Yes, he's a (good) friend of mine" = "Yes, I am a friend of his." = "Yes, we are friends."

Psychology Note: It may be interesting to consider a connection between psychology, persuasion, and identity in these language elements. Consider that we change "friend" to "fan", and suppose PersonA says to PersonB, "I am your fan." If this is believed, then a relationship is established:

• { PersonA, PersonB } = { ResourceSupplier, ResourceConsumer }

However, if PersonA says to PersonB, "You are my fan", and if this is believed, then

• { PersonA, PersonB } = { ResourceConsumer, ResourceSupplier }

Where "resource" can be anything from "time", "effort", "admiration", "money", "facebook fans", "twitter followers", etc.

Checking the definition of into:

1) from the outside to the inside of; to the midst or depths of" ⇒ walked into the house, jumped into the lake"

you can see that the destination is within something (the room or the lake in the examples).

But you cannot be within/inside of a window in this context.

In another context, such as:

I fell into the window.

by definition 4 - (so as to strike; against" ⇒ to bump into a door") this would be OK.