Eric Raymond (esr) has created reposurgeon, “a command interpreter for performing tricky editing operations on version-control histories.” The tool includes scripts for various purposes, including cleaning up the results of VCS conversions. Check it out from https://gitlab.com/esr/reposurgeon.
As of version 2.0 it includes support for reading SVN dumpfiles for complete and idiomatic translation to Git, Mercurial, etc.; see http://esr.ibiblio.org/?p=4071 for details. Reposurgeon has been used to convert several large projects to Git, including Emacs whose repository, ESR says, “is large, complex in branch structure, and old enough to have begun life as a CVS repo. That last part matters because some of the ugliest translation problems lurking in the back history of Subversion projects are strange Subversion operation sequences (including combinations of branch copy operations) generated by cvs2svn.”
(The git-svn tool included with Git will handle many Subversion repositories, including branches. It’s pretty commonly used, especially by teams that are in the process of doing a conversion, since it allows Git to behave as a Subversion client. But see ESR’s Don’t do svn-to-git repository conversions with git-svn!, where he discusses the drawbacks to git-svn as a conversion tool.)
Regarding your second question, it isn’t branching where the power of Git is so helpful (though Git is at least as powerful as Subversion in this regard); it’s when it comes to merging those branches that Git shines. Read through the Git Community Book, especially the section in chapter 3 titled “Basic Branching and Merging” and the section in chapter 7 titled “Advanced Merging”.