Icu care in hospitals. Is it pretty safe or do people frequently end up with mrsa?

Many complications. Generally care in icu's is accompanied by intense efforts to control secondary infection. The problem is that most patients in ICU have severe medical issues often requiring medications and techniques of management such as intubation of lungs and bladder, central IV lines, and so on, and these predispose to secondary infections. Mrsa is one, c. Difficile colitis, uti, pneumonia, etc., etc.
Common. Patients can have MRSA in the hospital or come in with it. Depends why the pt is there. More common now in the outpt setting as well now. In the ICU one has multiple devices inserted and any one of these may get infected. Everything is a potential source of infection. Good hand washing is a must for all!
Safe. It is possible to become infected with MRSA while in the hospital, but it does not mean that everyone who goes there will be infected, great precautions are taken to reduce hospital infections; however the possibility do exist.