I really need you to check these sentences please.Thank you.

1) A group of his fans were (not was?) waiting outside his flat.
2) While he was walking across the square, he stopped to sign a record for Mark Chapman.
3)When he returned home, Mark was still there in the square. He was hilding a gun. He called John Lennon by his name.
4)While John was turning around, he shot him five times. After he had shot him dead, he didn't run away.
5) The police officers arrested him while he was reading a book (on a bench).
6) Go straight on as far as the traffic light(s)/until you see/get to the traffic light. Then turn right (take a right/take the first turning on the right). You'll see the museum on your right.
7) Cross the street (go across the street) on the zebra crossing.
Go past the level crossing
When can I use "head" instead "go" to give directions?
Examples: Head north/south

1) A group of his fans was waiting outside his flat. (The subject is "group" which is singular, so "was" is the correct verb form.)

2) OK

3)When he returned home, Mark was still there in the square. He was hiding a gun. He called John Lennon by his name.

4)While John was turning around, Mark shot him five times. After Mark had shot him dead, Mark didn't run away. (With this phrasing, the "he" and "him" references are not clear.)

5) The police officers arrested him while he was reading a book.

6) Go straight until you get to the traffic lights. Then turn right. You'll see the museum on your right.

7) Cross the street on the zebra crossing. Go past the level crossing.

When can I use "head" instead "go" to give directions?
Examples: Head north/south
~~>After turning right, head north until you get to the hospital. (or something like that)

In #3, the first "he" needs to be clarified.

1) The sentence is correct. When referring to a group of people as a whole, "were" is the correct verb form to use. So, "A group of his fans were waiting outside his flat" is the right sentence.

2) The sentence is correct. The use of "while" indicates an action happening at the same time as another action. So, "While he was walking across the square, he stopped to sign a record for Mark Chapman" is the right sentence.

3) The sentence is correct. It describes a sequence of events in the past. So, "When he returned home, Mark was still there in the square. He was holding a gun. He called John Lennon by his name" is the right sentence.

4) The sentence is correct. It describes actions happening in the past. So, "While John was turning around, he shot him five times. After he had shot him dead, he didn't run away" is the right sentence.

5) The sentence is correct. It describes an action happening in the past. So, "The police officers arrested him while he was reading a book (on a bench)" is the right sentence.

6) The directions in the sentence are correct. You can use "head" instead of "go" when giving directions. For example, "Head north/south" is equivalent to saying "Go north/south." It indicates the direction the person should go.

7) The directions in the sentence are correct. "Cross the street on the zebra crossing" means to use the designated pedestrian crossing. "Go past the level crossing" means to continue beyond the railway crossing without crossing it.

You can use "head" instead of "go" when giving directions to indicate the general direction someone should take. For example, "Head north" means to go in the direction of north. It is often used when giving compass directions.

I hope this helps! Let me know if you have any more questions.