Couple questions for those who have been around the network longer.
Are we allowed to create our own swag?
If we are allowed what all artwork do we have available to us?
We are not allowed to use SE design elements without permission. From the guidelines:
We generally do not permit use of our name or logo on merchandise.
Do contact Stack Exchange Inc. with a detailed proposal if you would like to request an exception.
Do not use the names or logos owned by Stack Exchange Inc. on any apparel or merchandise without our permission.
They say "logo" here, but I believe that would apply to all elements of the design -- putting the robot on a t-shirt probably won't fly. Notice that the footer of every page includes this:
site design / logo © 2016 Stack Exchange Inc; user contributions licensed under cc by-sa 3.0 with attribution required
When Mi Yodeya started its publications project, we asked for and were granted permission to use the logo, including in an altered form for one publication. (An SE designer even helped us with implementation.) So permission can be obtained, but you need to ask and it sounds like conventional applications like t-shirts might be declined. Something more closely tied with the site might be allowed, as it was for Mi Yodeya; that's up to SE.
So I filled out the contact us form asking about swag, and got this reply back:
We create swag for every site once its design has been launched, and it will be sent to the top 72 users of the site once the swag designs have been finalized. You'll see a post about it on meta once it's ready, and we will contact all the eligible users to request shipping information.
Stack Overflow Team