I need you to check these expressions.

1) Don't keep/leave them waiting outside. Try to hurry up.
2) I suggest your going to the chemist's.
3) In my town there are two chemist's, a tobacconist's and two cafes.
4)He excused my arriving late.
5) The technician got/had this machine going in no time (I need to rephrase got/had).
6) I always delayed his going to the dentist's (I don't think it is possible but I need to provide an example with delay + possessive adjective+ gerund and pardon + possessive adjective+ gerund)
7) Beside being friendly, she is also generous.

1. (either verb works)

2. better: I suggest you go to the chemist.

3. In my town, there are two chemists, a tobacconist, and two cafes.
OR
In my town there are two pharmacies, a tobacco shop, and two cafes.

4. OK

5. The technician got this machine going in no time.

6. The student delayed his arrival by purposely missing the 8:00 train.

Before the murderer could be executed, the governor pardoned him for his crime.

7. OK