To all your questions: don’t use plugins. Use FTP instead.
FTP supports secure connections and FileZilla will use it by default. It’s pretty much as unrestricted as you can get in terms of upload capacity (respecting the file size limit, storage limit and inode limit, of course). And it’s the recommended way to migrate a website both by us and by WordPress.
So please step out of the idea of trying to solve every problem by piling on more stuff on WordPress. That kind of behavior will cause a lot of issues with bloat, bugs and so on.