Heard of it. It's not typical, but I have heard of it happening. This kind of relationship is complex. It is impacted by temperament, parental involvement (or lack thereof) family politics, shame, and rage, just to name a few factors, but there are others.
Yes. This is common and normal and part of a typical sibling rivalry. Oftenthe older and bigger sibling gets the best of it until the younger child achieves similar stature. However, teach the older child that the behavior is unacceptable and set clear limits on what is tolerated. Stop obviously bullying without warning every time. Appealing to 'feelings' likely wont help but consequences will.
It happens. Siblings bully one another sometimes. Usually it's the older one doing the bullying, but there's no rule. That said, i like to view any bullying as an opportunity to teach both children empathy: "how do you think your brother felt when you hit him? Do you think his feelings were hurt? How do you think you would feel if someone hit you?".