Legal Question in Intellectual Property in Texas

Yes and Yes. Of course the copyright would have to be by the author, which is most likely the school under a work for hire authorship. The logo and verbiage are trademarks, also. And, both copyrights and trademarks apply automatically without registration, although registration is a prerequisite to the most effective enforcement. Certainly the district can sign with a single vendor, and usually do in order to obtain volume pricing. Since it is their logo and their verbiage, not yours, they can require you to go to their authorized suppliers or you risk committing trademark and copyright infringement. For colleges, say Notre Dame or USC or University of Texas Longhorns, this is a major source of revenue that they watch closely and students can also get expelled for "cheating" on logos.