Yes. You can set a date to accept offers.
As for the number of days you have to counter, that depends. Often, offers include an expiration date. (It's a good idea, from the buyer's perspective, in most cases to include an expiration date.) If, for example, an offer expires in 72 hours, then you either accept the offer in that time period or it expires. Actually, a counter establishes a new offer, so if you receive an offer and counter it (whether or not it's prior to a stated expiration date), you've really created a new offer and the original offer by the would-be buyer is null and void. So, from that perspective, it really doesn't matter when you counter. As a practical matter, an offer should be countered promptly. A would-be buyer can always withdraw an offer, so it doesn't pay to sit on offers, or to shop an offer around in hopes of getting a more favorable one.
Your Realtor can provide more information.