Конечно, вот перевод этих предложений в косвенную речь на английском языке:
My doctor advises not to take this medicine.
- My doctor advises that I should not take that medicine.
David says that he saw that movie, but he didn't like it.
- David said that he had seen that movie, but he hadn't liked it.
They are wondering what else Mr. Brown said.
- They asked what else Mr. Brown had said.
Mom asks me to clean the room once a week.
- Mom asked me to clean the room once a week.
Kate is asking if the others know about the changes in the plan.
- Kate asked if the others knew about the changes in the plan.
Mr. Black says that he was walking home at that time and saw everything.
- Mr. Black said that he had been walking home at that time and had seen everything.
My little sister says that she will be a doctor.
- My little sister said that she would be a doctor.
The teacher always asks us why we are late.
- The teacher always asked us why we were late.
I am wondering who is responsible for this work.
- I wondered who was responsible for that work.
Susan is asking when your brother was born.
- Susan asked when your brother had been born.
Обратите внимание, что в косвенной речи время обычно сдвигается на одно прошедшее время назад, если это возможно и уместно в контексте.