So far, I've created a process where the initiator creates a new contract, uploads the word document, enters contact info of vendor and Submit. I receive the email and then I hit forward and Joget sends the email to the vendor. 

You can instead send the assignment link to the Userview Inbox to your vendor, so that your vendor can view the assignment and respond directly from there. There's no need for the hassle of forwarding mail and subsequently.

I want to create an independent batch job, that periodically checks my email. and once it receives the appropriate email, pick up the appropriate process and update the signed document. 

If you want to do it this way, you will need to write a piece of code to crawl a email server that expects the delivery of the email, matches its contents, and integrate with Joget, e.g. assignment completion API so that you can continue your work in Joget.

I can't send the assignment link to Vendor because they're not part of my company. Therefore, I cannot provide them access to the link. I understand that I would need to write a code to crawl the email server, but does Joget provide a framework to create independent batch workers. Something like a plugin approach. If Joget is an app-building framework, should independent modules such as a batch processor do it? The reason I'm asking is because I have to send a weekly report of all pending contracts to my boss. Again, this is an independent task that is outside the process described above.

Have a look at http://dev.joget.org/community/display/KBv5/Email+Polling+System It is doing something similar as what you described here.