This is basic information/language he will be using at the preschool program and it will eventually be part on the way you talk to him. You want to be on the same page as the school so he won't become confused. If you tell him time to pick up and then don't use the same language as the pre-school it only makes things harder for him.
The way she is teaching him is normal. He needs this to help him learn the value of time, how long 5 minutes is, how long 3minutes is, etc...kids learn the concept of time passing by this. It is an important part of the pre-school learning program. That's why they all use this concept to get the kids to clean up and do just about anything. It gives them a chance to mentally prepare for transitioning into another activity and do the required task.
I don't have an opinion that is strong one way or the other about signing. If you want to sign with him then sign up for some classes and learn the signs. You will be teaching him and then that will strengthen the signs for you too. If you call the school board they most likely have at least one teacher who works with deaf children as a translator in classes. That person will be able to get you headed in the right direction to finding classes and other resources to fill the needs you have. They may even work with you one on one. You can also buy videos and other items at book stores like Amazon or Hastings. They can be very good too.
As for him doing what she wants, if he is responding then he is paying attention to her whether she is speaking loudly or not. He may be learning to read lips and that way make out what is being said. If he is not paying attention to you then make sure he is looking at your lips when you are giving him directions.
Putting him in timeout for not listening is not a bad thing if it is for just not doing what you ask. If he is paying attention and choosing to not mind then he needs consequences. If you think he can't hear you then make up some pictures of the activities you want him to do and show him the pictures and point. When you learn the needed signs use the pictures and the signs together and he'll understand the sign better.