Is there a difference between OS in
speed of database management?
Is there an OS which works best when
combining 20+ servers?
Is there an OS best for video
These questions are in some sense non-sensical. The question you want to ask is how to evaluate particular solutions. All installations has peculiarities that will impact performance far more than choice of operating system. Thus, the only thing you can do is evaluate and test on staging installations that try to mimic the production environment you envision. So, for example, you may want to ask: "How can I comparably measure performance of MySQL on Windows and Linux?"
What OS is best for safety?
The one whose security mechanisms you understand and maintain.
What OS is most stable and recommended
for use in professional website
I dare say the majority of web servers connected to public Internet runs Linux. Tons of info on this can be found at http://news.netcraft.com/.