Let's say that I have an SSH tunnel and my private encryption key. The server has my public key which it uses to encrypt data sent to me. Does the information that I send to the server also get encrypted? Does the SSH server send me it's own public key through the downstream when I connect to it?

wulp,
Once you put your public key that was created with ssh-keygen (it is at ~/.ssh/id_rsa.pub) on the server at ~/.ssh/authorized_keys, then log out and log in again, SSH will use the files in the ~/.ssh directory to authenticate you. During the session setup, a session key is created and shared. Now you will no longer be using public/private asymmetric encryption once the session key (actually keys for each direction, client-to-server and server-to-client, and separate keys for encryption and for integrity checking), meaning the symmetric secret, is shared. Bulk encryption is done using the session keys, not the public and private keys.
If you do an "ssh -vvv user@server", you can see everything done in the session setup. It will help you if you can follow along to see what each of those lines in the debug dump means. I recommend that you buy the book "SSH, The Secure Shell: The Definitive Guide" (Second Edition) ISBN-13: 978-0-596-00895-6.
You can prove to yourself that data are encrypted in both directions by setting up an SSH session in one terminal window and, in another terminal window, running "snort -vde" as root.

This might also be of interest to you: https://en.wikipedia.org/wiki/Diffie...n_key_exchange

SSH was designed to establish connections in a secure manner under the assumption that it is operating in a hostile environment.

Public-key encryption (PKI) techniques are computationally expensive, and would be weakened if very large amounts of data were sent using them. Therefore, PKI is used only in the initial "handshaking" that is used to initiate the conversation -- and that may from time to time thereafter be used during the conversation. This handshaking establishes:

1. The mutually acceptable identity of the two parties who are communication. ("Alice, is that really you?")
2. The conventional cipher algorithm that is to be used.
3. The secret key that is to be plugged into that cipher.

You see similar techniques being used in simpler crypto situations, such as the ones that are commonly used to secure (sic... ) wireless networks. The encryption hardware is built into the device itself; the weakness of the original technique was that it used a single fixed, unchanging key. (You could brute-force the algorithm and, once you had done so, you could eavesdrop on everybody in the coffee shop.) The replacement algorithms use a software agent to conduct a preliminary key-exchange. The same fast hardware is still used, but everyone's key de jour is different and subject to change.