When you ult with malz can you keep using your moves or will that cancel your ult stun?

Most things (including your other skills) will cancel your ult while you're using it.

You can, however, use ignite. I'm also fairly sure you can use most item active abilities, including Deathfire Grasp's. A word of caution, though: the range of your ult is longer than the range of ignite and Deathfire Grasp. This means that, if you used your ult at maximum range, and then try to use ignite during the cast, Malzahar will move forward to attempt to use ignite, thus canceling your ult. This is very frustrating, so ensure that you are within ignite range, or wait until you've finished channeling if you're worried.