Yes, you can create multiple pipelines for different branches on the same repository. This is useful when you want to have multiple testing environments for different departments. One common schema for this is to have these:
Local development -> Q&A Team testing -> User acceptance testing -> Preprod integration -> Production
Usually these are different servers, but if you don't have multiple servers at your disposal I guess you can create multiple instances on the same machine.
As for the other questions:
Yes, is a good approach if you need multiple testing instances that should not interact with others instances ( be mindful that this requires different persistence storage for each instance ).
There are many strategies here. For new branch you have to ask yourself "Is this feature related to anything from staging branch or is separate ?". If is related, you make a branch from stagging, else you make it from master.
Also as a side note, I see that both master and stagging deploy to a test environment ( deducted from name ). Where will be the production code kept ? You need a base branch which holds the currently deployed to production code in case you need to redeploy after a failure or to make a hotfix. Most common strategy is to keep master as production branch and make one or multiple release branches, which I think would fit for your stagging branches.