MRSA is contagious, that is why she is on isolation precautions to prevent the spread of MRSA to staff, visitors and other patients. It is spread via contact. To protect yourself and others you should follow hospital policy and wear gown and gloves when in the room, wash your hands thorouly prior to leaving the room. It is not a good idea to kiss your grandmother goodbye. It sounds like the MRSA is contained to her nose, you can only contract it if you come in contact with the infected area - her nose or nasal secretions or even secretions from her mouth. If she rubs her hands on her nose and gets secretions on her hands you could catch it or spread it to others that way, same with secretions on pillows, etc...
Many nurses and other hospital workers as well as people in the public are colonized with MRSA - meaning they do not have an active infection. MRSA is mostly a concern when someone who has compriomisted health, an open wound, etc... if it is in an open wound it will prevent healing. Your grandmother healthcare team is most likely taking precautions to prevent the MRSA from spreading to the comprimised (sp) area in your grandmother's throat. I am sure that she is on antibiotics.
Please talk to the nurse about MRSA she/he should beable to provide you with some reliable written information. Also check out a reliable website such as the Mayo Clinic and see what they have to say about MRSA.
As far as receiving 2 units of blood - the doctor will re-check your grandmothers blood count and if it is still low and meets criteria for another transfusion she will get one. Most likely she only needed the 2 units and is fine now.
Wishing your grandmother a quick recovery!