They are both right, but they have different meanings.
"Do something for me" is when you want someone to do something that you need or enjoy. It means do me a favour, do something to help me, do something for my sake or for my benefit. Often it involves an inconvenience on the part of the doer ( as in "Can you do something for me? Can you call in at the supermarket on your way home from work and get me some avocados?") or even a sacrifice ("I wanted to stay living in the countryside, but you insisted on moving to the city. I never wanted to give up my farm and become an office worker. I did it for you").
"Do something to me" means to do something which has an effect on me. It's occasionally something positive (for example, you might love the way that your wife rubs your back), but it's more often negative. If your brother hits you, your business partner cheats you out of money or your friends gossip about you, these are things which they do to you, with negative effects.
"Read to me" simply means that other person wants you to listen to something they're reading : you may or may not want to listen.
"Read for me" means that you would like the other person to read something, either to help you or to give you pleasure. If you read something for someone, you are helping them in some way. We'll often read something for another person if they can't read it themselves.