Ответ:

1. Someone cut Kate’s hair at 13.30 pm.

Kate had her hair cut at 13.30 pm.

2 The mechanic is changing Peter’s car battery.                

Peter is having his car battery changed.

3 The hairdresser dyed my mother’s hair last Saturday.                

My mother had her hair dyed last Saturday.

4 Someone checks Henry’s guitar after every show.

  Henry has his guitar checked after every show.