Learn English – There is a family of 4 people – is it right

Yes, "There is a family of four people" is fine. In fact, you could even exclude "people" and it would be fine, as it is implied that the family is comprised of humans. I'm going to include the rest of your original phrase because it makes the sentence make a little better sense. It's not wrong without it.

There is a family of four sitting on the bench.

This will pretty much always mean that the family is all present, sitting on the bench.

Your third sentence is a bit more complex. There are a couple of options here but I would say, as is, it's not a good construction.

There are four people family.

Option one is to add "in that/this" to the sentence:

There are four people in that family sitting on the bench.

This sentence can be very ambiguous. If said aloud, the stress put on different words can make it less ambiguous. There are three things I can think of it meaning:

• There's a family sitting on the bench (of which only 2-3 may be present) but you are saying that, regardless of the number on the bench, there are four members in the family.
• There are four people, who are all in a family together, sitting on that bench... with the implication that there are other people who are in the family but who are not physically sitting on the bench.
• There are four people who are all sitting on the bench who are also in a family together (I would argue the first two possibilities are more likely)

Option two is to make "family" singular and turn "four people" into a modifier of the family. When you use "four people" as a modifier of "family", it should actually be "four person" or "four-person".

There is a four-person family sitting on the bench.

This means the same thing as the original sentence, all four members of the family are present and sitting on the bench.