What happens in the child branch if I delete a parent branch in git

Simply use git format-patch origin -o {output_folder}.

After getting all the patches out, go to the master and create a new branch.

Then apply those patches as so: git am {output_folder}/{patch_name}.patch.

Then after verifying you didn't loose any info, you can delete the old branch with git Branch -D {name_old_branch}

What happens? nothing.

If you create a branch where another is, you can "delete" that other branch without losing anything. A branch (HEAD) is just a pointer to a commit.
As long as those commits are referenced by a branch HEAD (or are part of the branch HEAD ancestors), they aren't lost.
And even if they are no longer referenced by any branch or tag, they are still in the local reflog for (by default) 90 days.

But, looking at the man page for git branch, this seems easier:

 git branch (-m | -M) [<oldbranch>] <newbranch>

With:

-m
--move

Move/rename a branch and the corresponding reflog.

-M

Move/rename a branch even if the new branch name already exists.