1. Private key is a random number generated from your computer to be used only by the person who generated it. Through formula the computer generates a Public Key from the Private Key to be used on the network. So if someone wants to encrypt a message and send it to me can use my public key encrypt the message and then with my private key I will decrypt it and read it.
2. I kind of mentioned it in my answer for question one but basically we can use the public key to encrypt messages and second use case is to use it as a digital signature to prove that WE are the ones who send the 1000 bitcoin out that day