A good question. IMHO The first question is possibly the 'online bully' gains something & many times nothing. They only gain something when something is offered in return. The question becomes what is that something offered in return. Then one must ask is it beneficial or is there a gain. Remember that cannot occur unless something is offered first.
Let's go back a moment. Bullying must have three components. Those are it must be social, it must be a reoccurring behavioral pattern & it must have a target. One question is if the target is a character trait, a difference of experience, e.g., apprentice contrast a journeyman, a positional stance & etc. or is it purely personal. If the target is a broad brush stroke, then it is not personal. It is then that it is a tactic or technique of intimidation of the engagement of difference rather than a personal attack.
One may discover with the two most common forms of online interactions - forums & chats, the seemingly bully of the broad stroke of the brush will not engage or continue engaging a person who finds offense with the tactic or technique. In other words they attack any of an opposing view with dissertations of any length, bantering of the logic, and etc., yet respect person's whose 'feelings' were hurt by disengaging.
The second question is absolutely not. The keyboard (symbolic representation of a process based on principles) creates. That is powerful. The result is force combined with time & how far it goes. At question is attraction.
The third question is absolutely. However, everyone has feelings. Feelings are the result of sensing. Feelings get hurt at times. Emotions arrive from feelings. One must precede the other. Yet, with online interactions we do not see, hear, smell, and usually only see an image if available, thus how can our feelings be hurt? There is the sixth sense to consider current psychology infers as intuition. Possibly that could be hurt?
What is left is cognition. Cognition is thoughts and memories. Therefore some or many may conclude when one's feelings are hurt of actuality it is the recall of a past event having the effect of reoccurring. An old wound or injury is opened up. Some say that is a gift or blessing offering the opportunity for more complete healing or resolve for the original encounter of hurt feelings. One solution for examining or reflection offering healing is 'Mindfulness' as a technique. Well worth researching.
Haven't we all said she/he reminds me of ???