Am I doing a propery use of git?
Yes the workflow that you describe is pretty much standard workflow. You create some branch, you work on it and when you’re done you merge it and remove the not needed branch (unless you are going to continue developing on that branch).
After removing a branch, viewing the history it seems to me that I
have lost every information about the branch itself… is that normal?
Yes this is normal.
is it possible to remove a branch but leaving the history information
unbroken?
Not sure what you mean here. As long as you have merged the branch before deleting it, the history is still there. You just merged it into another branch and the history can be seen on that branch. There is no way to know when a branch was deleted if that’s what you are asking for.