With Git (as with any DVCS) you have a whole standalone copy of the full repository locally. (Except if you do a shallow clone, or change the refspec so that only specific branches are cloned).
git clone
creates a local branch for the remote branch that is the default branch for that repository (HEAD
in the remote points to it) which most often is master
as it is the conventional default.
If you don't want the default branch created, you can tell git clone
via parameter which branch to create locally after cloning.
Either way you can at any time create local branches from any remote branch you want and name them however you want. All remote branches are in your local repository as remote tracking branches, you just do not have local branches for them by default.
That there are deleted files shown directly after a clone is nearly impossible as to my knowledge. Modified files could possibly be shown if you clone to Windows and there is some line-ending mangling going on. But deleted files should not be possible without you deleting the files.