/'dʲeləjɪt/ or /'dʲeləɪt/ (loss of /j/ before /ɪ/ is an ongoing process, not all speakers drop /j/ before /ɪ/).
In speech, /əɪ/ might or might not sound like a diphtong. However, we don't usually call it a diphtong because it's a result of the phonetic reduction and not a diphtong phoneme. Also, what exactly is pronounced depends greatly on the speaker and on the speed of speech.
In fact, "are /Vɪ/ and /Vj/ pronounced in the same way?" (worded 'is войны /'vojnə/ and воины /'voɪnə/ pronounced in the same way?') is a common flame war on a forum I frequent. :D There's clearly no agreement on this, some people insist that /ɪ/ is not creating a diphtong, others insist it does.
This course systematically translates Russian accusative without 'some', and uses 'some' for translating Russian direct objects in genitive (мама сделала сок = mum made [the] juice, мама сделала сока = mum made some juice). I think the course authors made a conscious decision to make those forms look different, and force people to remember the difference.
Сок (sok) and компо́т (kompot) are different things. Сок is extracted from fresh fruit. Компо́т is mady by boiling fruit, usually dry fruit, with adding sugar.
Also, сок is usually made from one kind of fruit, while компо́т is usually made with several kinds.
No, you can't use the genitive case with the partitive meaning here. It's only possible for perfective verbs (like сделает), but not with imperfective verbs (like делает).
- Nominative case is only used for subject. It can sometimes follow the verb, but only if the sentence begins with something other then subject: e.g. with a direct object (Сок делает мама 'It's mother who is making juice'), with an indirect object (Мне нравится Сергей 'I like Sergey', literally To-me is-likeable Sergei), with an adverb (Завтра придёт Инна 'Tomorrow, Ivan will come'), with a prepositional phrase (У меня есть мечта 'I have a dream'), or, basically, anything that is not a subject.
- Accusative is the normal case for direct objects in positive sentences (e.g. Я купи́л руба́шку 'I've bought a shirt'). In negative sentences, it's required for living beings (e.g. Я не встре́тил сестру́ 'I haven't met [my] sister').
- Genitive is used with partitive meaning in positive sentences (Duolingo generally translated this with 'some': Я купи́ла руба́шек 'I've bought some shirts'). In negative sentences, it's required for abstract'ish things (e.g. Я не потеря́ла наде́жды 'I haven't lost hope').
The most complex case is choosing between genitive and accusative in negative sentences. In the past, genitive was required. Now, it's slowly being replaced by accusative. The process is unfinished, and with some words, accusative sounds better, while with others, genitive sounds better
Yes, you can use prepare or cook. - all of this words translated as "готовить", but prepare can be used in other cases "Mother prepare documents" (Мама готовит документы), cook - translates also as "готовить" (in English you use it for food, but in Russian it is the same word).