Is MRSA serious and can it be transmitted by human skin to skin contact?

Yes, but. Mrsa is easily transmitted by skin to skin contact. That being said, staph aureus normally lives on our skin, and for the most part, it causes no issues. If the recipient is already sick, immunosuppressed, or otherwise has a poor response to staph aureus in general, they are at higher risk of actually having invasive disease vs. Just colonization.
YES and YES. Mrsa is a bacteria that is resistant to a number of previously effective antibiotics by mouth to treat "staph" infections. Mrsa can be aggressive and cause severe soft tissue infections and can kill a patient if not treated in a timely fashion with the appropiate antibiotics. Mrsa is commonly found on the skin of certain people can spread by skin-to-skin (direct) or by fomite (indirect) contact.