According to the project's legal page,
Most pieces of software from VideoLAN are licensed under the GNU
General Public License Version 2
So, to take your question by parts, and bearing in mind that IANAL/IANYL:
Yes, you would violate the GPL;
Yes; specifically, your app must be licenced under either GPLv2 or a licence which is at least as permissive (referred to as a compatible licence) - in my opinion, your life will be simplest if you pick GPLv2 also;
Yes, you need to comply with all the provisions of GPLv2 with respect to the vlclib codebase, and all the provisions of the licence you choose (see part 2) with respect to the other parts of your product, assuming you wrote them all, and retain the copyright thereto.
Note that this analysis presumes that linking with a library creates a derivative work, and this has not yet (to my knowledge) been ruled on by a court. I wouldn't bet my house on it not doing so, though.