"is it needed to drink a lot of water?" Less popular, but valid here, I think. http://english.stackexchange.com/questions/112508/difference-between-needed-and-necessary
"Is it needed" sounds really bizarre to me. If I heard someone say your sentence my first thought would be that you're asking if you need some object to be able to drink a lot of water. Here's someone else's explanation with a couple other examples:
"It is necessary (=must be done) to peel vegetables because the outer skin is not edible/for hygienic purposes/because they cook more quickly without the skin.
It is needed to peel vegetables.
A person does not scratch off the skin from a potato with his nails, nor rub it with sandpaper. There is a special kitchen tool called a vegetable peeler. I bought one because it is needed (=required for the purpose of peeling) when you peel vegetables.
'It is necessary for me to go to Tokyo tomorrow to discuss a business contract in person.'
In other words, 'I have to go to Tokyo tomorrow...'
'It is needed to go to Tokyo tomorrow.'
'His Japanese is rusty. Where is the office copy of the English-Japanese dictionary? It is needed for when he goes to Tokyo tomorrow so he can take it with him.'"
There are certainly situations where you can use "needed" and "necessary" interchangeably, but I don't think it works here.
Good detectiving (inventing words is fun!)! Yes, precisely.
"Is it mandatory/obligatory" - I would see these as impersonal, unless there were specific context (and "is it necessary" can be the same).
"Is it required" - I would say this one depends almost entirely on context and how I would interpret it initially without context would pretty much depend on the mood I'm in.
For good measure, I'll throw in my views on a few more related words:
"crucial" - Again it could really be either, I might be slightly more likely to guess impersonal with no context.
"vital" - Could easily be either, but probably "is this (object) vital?" in a contextless situation.
"expedient" - Impersonal.
"needful" - Almost certainly impersonal.
"compulsory - Impersonal.
"fundamental" - Likely impersonal, again context would clarify.
"imperative" - Probably impersonal.
It doesn't really fit the pattern that well, but to me, "needed" simply doesn't work impersonally in this construction. If you can see any logic, I'd love to hear it, because I can't find any!
I think "should you" should be accepted as well. It's not exactly 'proper' English, but it's what you would naturally say. In fact, I did it just now - "it's what YOU would naturally say".
Nobody says "one" unless they're very, very formal. If this were an English course then perhaps we should be strict. But while I'm learning Polish I don't think I should focus on what Lady Winterbottom would think of my grammar.