"Tomatoes, cabbages, carrots, and pumpkins are vegetables."
Translation:Tomat, kubis, wortel, dan labu itu sayur.
In isolation, /adalah/ does NOT have the same meaning as /itu/. /Adalah/ is a copula verb for linking nouns to other nouns (and occasionally linking nouns to adjectives, but that's far less common), and /itu/ functions either as the demonstrative pronoun "that" or "those" (if the noun(s) to which /itu/ is attached are plural) or like the definite article "the" in English.
I can't speak about the difference on when to use /itu/ over /adalah/, but /adalah/ is what's called a copula. In English, we'd translate /adalah/ as a form of the verb 'to be'. Typically, in bahasa Indonesia (i.e. the majority Indonesian language) /adalah/ is used in identity and classification statements, so it can't be used with adjectives, but it can be used with other nouns. For example, "That man is a teacher" or "This person is my sister." Respectively, that looks like /Laki-laki itu adalah guru/ and /Orang ini adalah kakak perempuan saya/ or alternatively /Orang ini adalah adik perempuan saya/ for a younger sister instead of an older sister, because Indonesia makes those distinctions. Then again, one could also use the more generic term /saudari/ for "sister" without referencing whether she's your elder or not, but I suspect that would be very unusual.
One difference is that "itu," "ini," and "-nya" can be used to end a noun phrase. Then if you have an adjective after that noun phrase, this signals that the adjective that follows is attached to and giving information about that noun phrase. For example, /Makanan itu enak./ is a grammatically complete sentence meaning "That (or The) food is delicious (or good)." Used in this way, "itu" in the preceding example signals the end of the subject, and what follows is the predicate.
/Ada/ is a verb with a few different meanings. When it doesn't have a subject in front of it, /ada/ means 'there is' or 'there are' or 'there exists' to note the presence or existence of something (when translated into English).
If it does have a subject in front of it, /ada/ means 'to have' something. For example, /Saya ada uang/ would mean 'I have money', even though you could also say it as /Saya mempunyai uang/ for the actual verb 'to have'.
/Apakah/ is composed of two parts: /apa/ which means 'what' and /-kah/ which is an interrogative particle for making questions. Therefore, you can also say /bolehkah/ for 'May I do something?' /Bolehkah saya makan?/ means 'May I eat?' Compare this with the statement /Saya boleh makan./ 'I may eat.' Basically, you can attach /-kah/ to the end of a lot of "helping verbs" in order to turn a statement into a question like this: /Bolehkah saya makan?/
Both /ada/ and /adalah/ are copulas in Indonesia (in English, depending on the context, they might both be translated as a form of the verb 'to be'). But they are used in different ways. /Adalah/ links nouns to other nouns to describe relationships of identity or categorization. /Ada/ typically is used to indicate the presence or existence of the word that follows it and doesn't usually take a subject, unless it indicates the possession of the object (noun after /ada/) by the subject (noun or pronoun before /ada/.