Should batch sheets include the date of review?

Without much information, I would say always date it.

Yes. In my experience, all paperwork should be reviewed within 7 days max- You need a review date in order to show that you are reviewing production paperwork in a timely manner. 

Every single piece of your HACCP plan should be reviewed................particularly production records!  How else would you know if there is an issue that no one on the floor caught?

Review date is not requirement. But you can add review sign column and can define in respective SOP regarding timeline of review i.e weekly etc so that each time you do not have to put date.