"I need to cook shchi."
Translation:Мне надо приготовить щи.
No. The distinction is called aspect, namely imperfective vs perfective aspect respectively. Almost all verbs (not nouns, готовить is a verb) come in pairs of one imperfective, one perfective. Often, the perfective is formed by adding a prefix, like при-, to the imperfective. However, the prefix depends on the verb, and sometimes it's not even a prefix. So, you will have to learn them by heart.
"Щи" can also mean "щёки" (cheeks). It is not used in such a way in modern language, but there are colloquial expressions like "давать в щи" meaning to punch someone in the face or "получать по щам" meaning to get punched in the face. Both expressions can mean to beat someone or be beaten in generally, not specifically in the face. Their use is quite specific though.
It used to be one of the possible realisations of this sound as late as a 50 years ago (pretty unpopular, tough). It was used in Saint Petersburg a century ago. However, by now 'SHCH' has long ceased to be representative of how this sound is pronounced by most Russian speakers of various accents.
"Shch" seems to be the most common romanization of «щ» in most modern systems (definitely not pronounced as such, though). Some others include "shh", "ŝ", and "šč". My phonetic keyboard accepts "sc". Still, I find it strange that the «щ» in «борщ» has been romanized as "scht".
Actually, there is not enough context, and, yes, there is a difference.
- "Мне нужно приготовить щи". The emphasis is on the result of cooking - "I need shchi to be cooked, and I should cook it".
- "Мне нужно готовить щи". The emphasis goes to the process of cooking. Also it may mean a recurring action. "I need to cook shchi, it will take some time, I will be busy during the process of cooking".
Нужно is a predicate word. The person whom it applies to is always in the Dative. Russian has its share of impersonal predicates that behave this way: many of these words also double as adverbs:
- Тебе нужно поспать.
- Мне холодно.
- Тебе жарко?
- Мне страшно.
Then it is followed by an infinitive of a verb. Here, it might have been приготовить ("to prepare, to cook, to get ready") or сварить ("to cook through boiling"). The latter sure seems oddly specific to English speaker—but in Russian we do actually use варить/сварить rather often (as opposed to things we bake, fry etc.)
Both are usual transitive verbs, i.e. they take a direct object in the Accusative. Щи is an inanimate plural noun, so its Accusative is the same as its Nominative: щи.
You could use мне нужно. Нужен is the form used with masculine nouns: Мне нужен ключ ("I need a/the key").
With infinitives (when you need to perform some action) the words надо and нужно are used. They are pretty much interchangeable, «надо» considered slightly informal. Which somehow does not prevent its use in literature and academic writing.
Well, it is a transliteration of a Russian word and is, probably, about as popular as the soup itself. I think, borscht might be a better known relatively unknown soup ;)