They will not have access to your Facebook profile
Deleting the friend request of someone means that you neither want to be friends with that person nor want them to access your Facebook profile.
They will not be notified
The other person will not be notified of such actions as deleting the friend requests.
They can send you another request
If you have deleted another person’s request, they will still be able to send you another request if you have not blocked them. (See, What happens when you block someone on Facebook?)
The request will disappear
If you do not want to delete the request and ignore it while not taking any action, you will still see the person’s name in your friend request section.
They will know you deleted the request
They will only get to know if they will try to send you another request; otherwise, not. The person who sent the request will only be able to send it again if the other person has deleted their request. (See Study Summary: Facebook makes you unhappy and jealous)