Why are people getting paid for doing so?
Because there is a market for it, media: magazine, newspaper, yearbook, web, advertising, personal collection, and other purposes.
Do all portrait photographers have strobes or other professional equipments?
Yes, pro portrait photographers usually has lighting system, in studio or outside studio. Outside, they usually carry light stand, tripod, strobes, umbrella, reflectors and portable batteries.
How does a professional photographer work? When taking photos of a model, do you tell her/him how to posture or is it her/his job?
Usually photographer directs the model to pose, especially if the subject is not used to modelling. if you take a picture of experienced model tho, like fashion, it is easier.
But most of the time, photographer is the director, because photographer has and should has a vision of the result.
there is a photographer that aiming for natural shots too, or photojournalistic style. The photographer will not direct but follow and observe what the subject do. Following the subject when they do their work is the easiest way to achieve this kind of style.
I also kind of have the feeling that a good portrait photo is 50% to the photographer and 50% to the model. (Not exactly like nature or macro photography, if you took an amazing shot of a butterfly, you don't share the trophy with it) If the girl is prettier and better at posturing, the photos will be more appealing. Photographers are not magicians in this kind of photography.
Yes, i agree, nicer looking or exotic model and a nice setting will be better than less nice looking model in a boring setting.
In the real world, portrait photographers deal with less nicer subjects.
It is the challenge that the photographer need to face all the time.