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I am interesting in this process:

First I'd like to make any in my development branch, than it should be pushed to Test (master) branch and, therefore, to production.

For me the process:

1. init commit
   then, make prod branch from master init commit
   then, make dev branch from master init commit

2. checkout to dev branch
   then, do any
   then, commit
   then, checkout to master
   then, merge with dev

3. Do tests
   then, commit
   then, checkout to prod
   then, merge with master
   

Is this a right way to use this way or not? If not, explain please the right process.

Thanks a lot

You are looking for something similar to the git flow workflow.
Read all about it in the following post by Vincent Driessen