If you received a friend request, then it is a specific account holder that sent the request, though the account could be a fraudulent copy of an account, or a bot-controlled account, or another person has taken over the person's account.
However, if it was just a friend recommendation ('people you might know') it would only require that the account is still active (i.e. not closed or memorialised) for the algorithm to suggest the friendship based on whatever criteria Facebook uses.
No, the other person would not be notified that you searched for that person, though it is possible that Facebook might flag it as a factor for suggesting that the person may know you.