If I download a YouTube video, dub it in another language, and reupload it on YouTube, can I be prosecuted by law (or can YouTube remove my video) for infringement?
Yes, assuming the material was given the standard license. You would be creating a derivative work, and only the copyright owner has the right to authorize creation of a derivative work. See the copyright FAQ for general information. The owner can file a DMCA takedown notice with YouTube and they will by policy notify you of the infringement claim and unless you file a counter-notice (you legally couldn't given the facts you're asserting), they will take it down. The owner can also sue you.
Yes. Unless you have the permission of the copyright holder, you are making an infringing copy of their work. A similar question - with work-arrounds is available here.