I'm going to tell my mother how I feel about having a half brother
How do you feel about having a half brother?
I feel happiness. I'm happy that my mother was able to find someone else to have a child with him
It is great that you are welcoming to the new family member.    Make sure that you understand how your mother may react to it and be prepared to respect her during the process.  Not doing so could cause deeper family drama.
I agree. I guess you can not put a time stamp on when someone is going to fall in love. I just wish it was with my dad.
Sometimes people fall in love and want to start a new family sooner than later. You don't have any right to tell her what she can and can't do. I understand you might be hurt by this but it's her life, try respecting her decision.