I know some. My mom had them and almost bled to death. Yes, they can start bleeding again. Ulcers are caused by many things, but there is evidence that they are caused by a bacteria in the stomach. They can treat him with medicine for that and hopefully that will eliminate his problems. Also, a change in diet will be necessary. My mom had to give up alcohol, juice, anything that is acidy. Stress can also be a trigger as well. It will take a bit of time for him to recover. He lost blood so he will be very tired and weak. I'm sure they are giving him transfusions at this time to build up his blood count.
My mom was in the hospital the first time for over a month. It took her about a year to fully recover. She had a couple of relapses. She didn't take her diet seriously and she missed my engagement party and Christmas. She was in the hospital for 10 days. She seemed to relapse around the Christmas holidays. She loved the holidays and would get all worked up. December - February were bad for her. After all this, every time she said her stomach hurt we all held our breath! She did take the medicine and it did eliminate the bacteria but she would NEVER take a chance and eat what she shouldn't. After her couple of relaspes she was very faithful to her diet.
I don't know much about MRSA. However, with your dad being in a weakened condition, that to me would make it a little more serious.
PM if you have any questions. I will keep your family in my thoughts and prayers.