Hi Alfredo,
You don't need to have the LabVIEW development environment installed in the deployment machines in order for TestStand to be able to call LabVIEW call modules.
You will, however, need to install the LabVIEW runtime engine, and either the TestStand Development environment or the TestStand Deployment engine.
Take a look at this https://knowledge.ni.com/KnowledgeArticleDetails?id=kA00Z0000019VenSAE&l=en-US.
When it comes to dependencies, the TestStand deployment utility can help you ensure that all dependencies are included in your deployment. I don't believe the fact that you are using DQMH is relevant, the deployment utility should still help, although I have not tried this myself. Take a look at this link https://www.ni.com/en/support/documentation/supplemental/08/teststand-system-deployment-best-practic....
There are some exceptions where the TestStand deployment utility can't automatically track dependencies. For example, when a vi is being called dynamically by providing it's path and being loaded into memory at runtime.
Hope the info above helps you get a better picture on how to successfully deploy your test software.