I am connected to my chat accounts via Empathy, a messaging program, and it has my password stored in it.
I am really curious to know how it is storing the passwords, and if there is any they can retrieved back in plain text? 
You are absolutely correct in your assumptions. 

If you are using a computer owned and operated by your employer, they effectively have full control over your communications. Based on what you have provided, they have installed a root CA certificate that allows them to sign a certificate for Google themselves. 

This isn't that uncommon in the enterprise, as it allows inspection of encrypted traffic for virus or data leaks. 

To answer your three questions:


Yes it is very possible, and likely. How active they are at monitoring these things is unknown.
Your password can be read in plain text by your employer. I don't know what you mean about the web server. 
You can check the certificate to see who signed it, as you have already done. You can also compare the fingerprint to that of Google (checked from a third party outside of business control)


Edit:


  How exactly is my employer able to unencrypt that? Could you perhaps
  elaborate on that a bit?


You are using the bad certificate to connect to an intermediary device such as the firewall, that device is then connecting to Google using the correct certificate. The communication is encrypted from your client to the MITM, decrypted, and then re-encrypted on its way to Google. 
