Is it legal for a workcenter to prohibit all types of drinks except for water?

Yes, it's legal. You see, employers can make any rule they like. Hair length, type of dress, food at your desk, etc. Employees don't have to obey them, but it may cost them their jobs. So your friend must decide whether drinking something other than water is worth his/her job.

Yes that is legal. Many work places have that rule at work stations. She has to be allowed to drink whatever she wants during her lunch break but during working hours at a desk they can make the bottled water rule only. That is legal. Many places dont want employees to spill items or have liquids with strong odors that might upset customers. Also coffee can make bad breath making it bad for her to interact with customers. She either needs to deal with the new rule or quit.

In a private company they can make rules about drinking only water at a work station while working. So if she likes coffee she needs to make sure she drinks it before work or during her break. I only drink bottled water at my job too because I work on patients and it is cleaner to have only bottled water around.

I do not see anything wrong with that. Coffee makes people hyper and sodas are loaded with sugar which is not only bad for your healthy but makes people grumpy. It is perfectly legal. Your friend can always leave.

i can't provide a reference since there is nothing to reference. There is no law about what you can drink and can't drink at work. This is left up to the employer.

Yes, they could ban even water if they wanted to as long as she isn't on break and in the public view.