I want to use chalk paint on my bathroom vanity.

You can! Just clean the surface really well and then paint. You don't need to sand or prep, that is the wonderful thing about chalk paint. Take the drawers and cabinets out/off and remove all hinges. Paint the doors and drawers in your basement or garage. Stand them up on empty boxes while painting them so they aren't on the floor, it makes them easier to paint. You are best to go over them with a wipe on poly or a water based polycrylic than wax, it will last longer.

I repainted my bathroom vanities with chalk paint last year, and they've held up very well. You don't need to strip or sand unless the vanity is in poor condition. Just remove the hardware, clean the vanity with a damp cloth to remove any dust, and apply the paint. Don't be afraid if your first coat looks thin and patchy. It will dry quickly, and then you can apply a second coat, and then a third.

When the paint is completely dry, you'll need to seal it by applying wax or polycrylic. I prefer polycrylic because it doesn't require re-application, but wax (I like Renaissance's micro-crystalline wax polish) adds luster, and colored wax (most people prefer dark) can highlight architectural detail. Use a natural bristle brush to apply the wax, then buff. Though the paint itself is low-odor, the wax needs to be applied under well-ventilated conditions.

This site offers more detail, including a link at the bottom to additional steps if you want to distress your piece: http://www.thinkingcloset.com/2014/09/22/the-beginners-guide-to-annie-sloan-chalk-paint/ Good luck!

Yes you can do it, but remember to wax it afterwards.

Yes you can use chalk paint; however because of the potentially high moisture area, I would seal it with polycrylic rather than the wax

http://therusticboxwood.com/2015/09/diy-chalk-painted-bathroom-vanity-makeover/

Yes, you can. Here's a good tutorial: http://www.providenthomedesign.com/2015/08/06/painting-cabinets-with-chalk-paint/