A number of these questions can only be answered by the staff at your university -- the license questions are related to what kind of license your university has, and if they have a cluster they likely have instructions on how to access it, how to submit jobs, etc.
To access and submit jobs to an existing cluster, your client only needs the Parallel Computing Toolbox license (use "ver" at the MATLAB command prompt). So if you have that and can find documentation for how to connect to a cluster, you should be able to submit jobs.
As for cluster creation, you can set up a standalone cluster using Parallel Server or integrate with an existing cluster. But that's a lot of work/effort compared to connecting to an existing cluster that's already set up, so it is a good idea to find out if there is existing documentation. Depending on how your university publishes documents you may be able to just google it with searches like "submitting matlab jobs to <university> cluster" or "using parallel server at <university>". These searches work for a number of universities I've tried.
While you are figuring out the cluster question, you can actually experiment on your local machine using the "local" cluster profile, which should require no setup and will be able to start workers, etc just like the cluster. When you figure out the cluster access questions, you can change the cluster profile to use the one for your compute cluster vs. local machine. So you can get experimenting right now.
