"Are you a student?"
No, not quite. Verbs aren't always at the end in the german language. Your sentence for exemple would actually be "I bought a big, red, fluffy chair, which is made out of polyester, from Ikea." = „Ich kaufte einen großen, roten, fluffigen Stuhl, welcher aus Poliester gemacht ist, von Ikea." In german you can put many sentences in the SVO structure, but there are also many senteces which have one or multiple verbs at the end.
Could be "Ich habe einen großen, roten, fluffigen Stuhl gekauft, welcher aus Polyester gemacht ist, von Ikea." so the first verb is split in two. Perhaps that would be "I have bought a big, red, fluffy chair, which is made out of polyester, from Ikea." in english. But I think bought and have bought and kaufte and habe gekauft mean basically the same?
あなた is the Japanese pronoun "you"
Usually pronouns are omitted and implied through context in Japanese, or a person's name is used. あなた is a polite impersonal pronoun that would be used if you need to clarify who you are speaking to if you don't know the person's name and is most commonly used in media broadcasts that address the audience. It does circle back around to being very intimate though and is used between couples similar to "dear/darling"
学生ですか - "Are (you) a student?" - 'you' is implied; without context this could also be "is he/she a student", "are they students", etc.
あなたは学生ですか - Are you a student? - 'you' is explicitly stated
Not necessarily, あなた is considered the most polite "you" pronoun, however if you know a person's name it is more polite to address them by that. Using a pronoun like "you" is impersonal so can be rude if you know a name and refuse to use it. あなた is very often used in formal situations like news broadcasts/speeches/announcements in which "you" is not a specific person but a general audience. It is also fine to use if you do not know the person's name and need to clarify who you are speaking to.
It also circles around to being very intimate, used in couples similar to "darling" or "dear".
When angry you'd be more likely to hear more casual forms of "you" such as あんた、おまえ (or very hostile/confrontational forms てめえ、きさま which you're more likely to hear in anime/manga which tend to use a lot of exaggeration)
"omae" and "kimi" are both casual ways to address someone and wouldn't normally be used in polite speech (です)
Both would be rude to use in polite conversation, especially with elders/superiors.
"kimi" is very familiar. Using it sounds a bit condescending in a "you are not dangerous" way and it is mainly used by superiors to their juniors/elders to youngsters. It also carries a level of intimacy so may be used between partners/very close friends. You'll see it used a lot in music/poetry/titles to sound poetic.
"omae" is even more informal. It projects the speaker as a superior and while kimi is condescending, omae can be blatantly rude if used in the wrong situation. It is mainly only acceptable to use among peers/close friends. It is best to avoid.
あなた anata is the politest way to say "you" but even that can be rude in certain situations and is generally avoided. It is both overly distant (if you know the person's name it is rude to act as if you don't) and overly intimate (it circles back around to being used like "dear, darling" between partners so using it with someone else can also imply a level of intimacy that is unwarranted)
Not necessarily 'only' but yes it can be used that way.
あなた is also the politest form of "you" and can come off as very impersonal and distant. It can be used with strangers if you don't know their name and need to clarify who you are speaking to, and is often used when speaking to a general audience such as in announcements/news broadcasts/speeches.
あなた is the polite pronoun "you"
Pronouns are impersonal though so should only be used if you don't know the other person's name (and also circles back to being intimate, used in couples similar to 'dear, darling'), and are often omitted entirely if it can be understood through context who you are speaking about.
か is a question particle, it turns the statement into a question,
いぬです - It is a dog
いぬですか - Is it a dog?
がくせいです - (someone) is a student.
がくせいですか - is (someone) a student?
Particles are used to indicate the function of a word in a sentence, usually marking how a noun relates to the verb. They are also postpositional, coming after the word they point to.
As for formality there isn't really much difference between formal and informal particles. In very casual/colloquial conversation some particles may be dropped entirely (just as spoken English we tend to omit words/parts of words)
か as a question particle is only used with polite form, with casual questions the question would be implied through inflection (raising pitch at the end like we would in English) or ending in a softer explanatory particle の
食べますか (polite) or 食べるの (casual)？ "Will you eat?"
There are many particles and many have multiple functions depending on context. Rather than list them all here I'll share this Japanesepod101 video that covers them pretty well: https://www.youtube.com/watch?v=UaI7UpOl-Xk
CotoAcademy also has a good cheatsheet for them here: https://cotoacademy.com/n5-n4-japanese-particles-cheat-sheet-guide-pdf-free-download/
あなたは explicitly states the pronoun "You" where as the second omits the subject and is just assumed "you" from the context in which it would be used.
Both answers should be equally accepted, though it should be noted that pronouns, especially ones like あなた "you" would only be used if you did not know the person's name and you needed to clarify who you were speaking to. If you know the person's name it is much more polite to use that instead, and if it is clear from context who you are speaking about it can be omitted it entirely.