It is recommended you do not install nprinting on the same box as qlik sense server as part of the installation you need to install a certificate generated from the sense box to establish the connection to it.
I have installed the no tinting on a server running qlik view and they have not interfered with each other.
If you want to test the publishing and import tasks in a way that doesn't impact your production tasks then having a seperate box makes sense you can get a test server edition which is cheaper than a production one and cheaper than adding another engine dedicated to testing.
There is certainly no auto deployment feature to copy the componenets from one environmnet to another environment that im aware off.
if you break your work down into
1. The data source (Qlik Sense/View) are you going to have seperate dev/uat/live apps? when is that ready for use?
2. The connection to it (depends on the above environment)
3. The import test (Test Users vs production users) Are you going to have seperate import files or just the one?
4. The reports (Are you going to just use preview to confirm layout and content?)
5. The Published task are you going to test this using just test users are you going to load test it? Having the test and live on same environmnet worries me as will my testing impact inadvertantly the reports already in production.
there are lots of levers to work and each companies deployment will be different dependent on their priorites and focus.
Are your reports going to change regularly?
How many will you have to create?
DEV/UAT/LIVE is probably the wrong question what you should be asking is how can I release in this case NPrinting changes in a controlled manner that minimising the risk to the business in a timeframe that is acceptable to the business.
Based on your requirement how many check points do you need? how many people will be involved in your process developing, testing and deploying? when what and how will they test? that will give you an idea of how to develop your process and indicate the environmne you need to setup.