Is data received after transmission immediately stored and can that be recovered?
Briefly, communication between two hosts/peers on a network occurs by means of network sockets. Roughly a socket is pair (IP,PORT) of numbers which uniquely identifies a host on a network. So, when a host A sends data to another host B on the network, B listens to a corresponding port for incoming data. Data (payload) comes byte-by-byte and when one byte of data riches destination B gets notification. At this point it is up to the application what to do with data: to store it on the hard drive or in memory. Nothing is stored in HDD or on some other device by default.

As for "sending an essay to a server" your are talking about file transfer protocols, in particular file uploads. Whether your file was stored on the server depends on the underlying protocol. For example recently people have started talking about resumable file upload protocol.

Your questions say that you should start learning from basic TCP/IP and HTTP protocols, and move towards more advanced and specific protocols depending on your tasks.