«Учи́тель уже́ хо́чет спать» would work too.
«Хо́чется» behaves roughly like «надо»* («учителю хочется» 'to [the] teacher, it's desirable') and requires Dative case forms (учи́телю), while «хочет» is a normal verb («учитель хочет» '[the] teacher wants') and it requires Nominative case forms (учи́тель).
* However, «надо» is technically an adverb, while «хочется» is a subjectless verb — this difference will be important in the past tense (надо forms past tense with the verb 'to be': учи́телю бы́ло на́до, while хо́чется forms past tense like other verbs with the -ся postfix: учи́телю хоте́лось).
Is there a subtle difference in meaning or maybe politeness between these two constructions? For example, I'm thinking about when ordering in a restaurant and saying <<Мне хочется...>> instead of <<Я хочу>> to mean "I would like..." instead of "I want..." (Or maybe that would be <<Я хотел бы>>).
In restaurant, you can use both. In fact, I would use «дайте мне, пожалуйста́, X» or even «мне, пожа́луйста, X» in a restaurant, not telling about my wishes but asking for some kind of food. There's nothing wrong with telling about wishes either, but I believe «пожа́луйста» (or «бу́дьте добры́», which means the same thing) is enough to make the sentence polite.
As for politeness, I believe the difference is neglibile. I think subjunctive forms come off as more polite (because of the conditinal meaning: you would want it if the speaker could provide it; but if they don't, your wish could be ignored).
Also, impersonal forms like «хо́чется» would come off as slightly more polite than «хочу». Impersonal verbs present the desire as something you don't control, therefore, it doesn't mean you definitely need it.
If I were asked to sort them by politeness level, I would say:
- мне хоте́лось бы (the most polite),
- я хоте́ла бы,
- мне хо́чется,
- я хочу (the least polite).
This is my personal understanding. I'm a native speaker, but I haven't read much about politeness in Russian, so please take the order above with a grain of salt.
However, I believe «пожа́луйста» (and using «Вы», not «ты») gives a sufficent level of politeness in most circumstances, and you shouldn't worry about other things much.
I believe ‘is already wants’ is not grammatical in English. You have two main verbs (‘is’ and ‘wants’), which doesn’t work. You need to keep only ‘wants’ and get rid of ‘is’.
(For other verbs, is + -ing works, but ‘is already wanting’ is not something people usually say.)
The Russian word for ‘sleepy’ is «со́нный» (feminine со́нная).
This is the most amusing and ridiculous error I've encountered on Duolingo. It refuses the word "tired" and offers a colloquial baby-talk synonym in its place?? I actually laughed out loud, but on a more serious note, tired should obviously be accepted — sleepy, I'm not so sure about. It is extremely colloquial.
"The teacher is already sleepy" is playing extremely fast and loose with the translation. In essence "учителю уже хочется спать" can be interpreted to mean that but it's a completely inaccurate translation. Спать is a verb, not an adjective. "The teacher already wants to sleep" is accurate and other. Near-enough translations are not helpful for learners.
"sleepy" can be сонный and "hungry" is голодный, although they are unusual to describe yourself in the present (it is more common to say мне голодно). Thirsty has a word, but it is almost never used unless in poetry (like thirsty for revenge or something along those lines). for that one I would recommend always saying нужно вода or надо пить.
We wouldnt say it that way in English either. But with my limited understanding of word order and given many Russian phrases do seem to order their words as you suggest here, I think your thoughts are perfectly reasonable even if it wasn't quite correct on this occasion. But as Duo says, we're still learning even when we make mistakes.