Is an agreement on a price and granting the buyer a grace period to decide on the purchase considered a sale or a promise, and is it permissible for the seller to retract the sale or increase the price before the end of the grace period?

As long as the person has not agreed to the price, the sale has not been concluded. Requesting a grace period and its acceptance is a promise that does not necessitate fulfillment, and there is no harm in retracting the sale or selling at a different price.