I don't know what would be causing the vibration, but I very much doubt that it is caused by the new cassette. The rear derailleur will need to be re-adjusted for the new rear wheel; my first guess for the vibration would be that the upper limit screw needs to be adjusted.

Changing from a 14-34 to a 12-32 cassette should not require changing the chain length unless the chain was already a bit too long before you switched the cassette.

Is the front derailleur issue new or did it happen with the old cassette too? I can't think of any reason a new cassette would cause those symptoms, but there's always the possibility.