Which one is the most correct one?

1. We had several reasons for not accepting his application. In any case, he was unable to produce the required documents.
1. We had several reasons for not accepting his application. To start with, he was unable to produce the required documents. Both, depending on the context.

2. There is a total restriction on smoking in public places in Los Angeles
2. There is a total ban on smoking in public places in Los Angeles.  As you have used the word total, ban would sound better here.

3. They all thought very greatly of my old colleague
3. They all thought very highly of my old colleague Highly sounds more natural.

4. You cannot have an increase in salary. It’s not questionable
4. You cannot have an increase in salary. It’s out of the question It's out of the question.

5. They put iron bars on the windows to prevent burglars to break in
5. They put iron bars on the windows to make it impossible for burglars to break in

To prevent burglars from breaking in // to make it impossible for burglars to break in.
 .
7. I suggested that we allow the children go to the cinema and see Troy
7. I suggested our allowing the children to go to the cinema and see Troy. That we allow

9. The job doesn't appeal to me very much. On the contrary, the money they pay is ok.
9. The job doesn't appeal to me very much. Mind you, the money they pay is ok Mind you

10. Our cab was delayed by the traffic what made us to miss our train.
10. Our cab was delayed by the traffic which made us to miss our train which made us