whose

It can also be used for inanimated objects. Did you know this?
"This is the computer, whose screen broke last week"

Well... Yeah I guess. Unless in writing, people tend to avoid any sort of relative pronouns. Too formal, too clean, for English. Interesting that you made the screen the subject of "break"... I suppose it's grammatically unnoticeable so it's fine...

To be honest I didn't understand when whom is used.

I would recommend against any even recognition of the word whom. It's only ever used by radical English teachers, who ONLY speak English, and don't ACTUALLY have any idea what a direct object really is. Кого is great. Russian has actual use for these things, but that ship has sailed for english a long time ago (sailed, crashed, and sunk). Its 100% word order now. Its at the point now where, if you DO say whom, it will often stop the conversation dead in its tracks and make the person give you a disappointed/confused look. "My boss, who I hate..." is the standard now. All the way up (on the formality scale) to newspapers have forgotten "whom". If you're writing legal documents, it'll be okay. If you're in a highly professional (perhaps more language based, such as legal) environment, using it can then seem more "educated", than know-it-all/nerdy/attention-seeking. When it comes to "whom" as in the object of a preposition: "Who are you looking at?" is standard, "At whom are you looking?" is pretty much an unheard sentence entirely.

I was under impression that contructions like "one/two/three etc. of whom" were pretty much well used in English. I might be totally mistaken of course.

I suppose you can find some more... "set" phrases with whom. Like "Many people went there, most of whom didn't know where they were." < this is considerable less bad. It would be taken as just "good writing".

Uh, I don't know who you speak with, but "whom" is a common word in English. I use it often. Sure you won't find it being used amongst teenagers and the like, but would you really expect them to use it properly? Most people, especially Americans, butcher the English language until it's an incoherent mess.