

Here that doesn’t change or help in any way. You’re the one on the contract for the Internet access, so you’re responsible. That’s it.
You can operate as an ISP, but the requirements and responsibilities that go with that make this a non-starter. From my (limited) understanding, it includes that if you can’t provide the identity of someone who is being sued (including piracy, but also any other law breaking), you’re responsible.

Compressing it with handbrake will probably not look worse. MPEG2 used in DVD is notoriously inefficient by today’s standards. Depending on the codec selected, it’ll be a fraction of the size with no visible differences.
Unless you mean to keep the DVD structure and playability in DVD players (including menus and everything), but I don’t think handbrake can do that.