You got the "для" meaning correctly, but "на" is more like "for" in English (although frequently means "on", "on top of"), i.e. "купи на обед" - buy for lunch, "приготовь на завтра" - prepare for tomorrow.
Your guess on "as" is not correct, that would be "как" (as).
"За" is more like "after (or behind) something", i.e. "Сходи за хлебом", - go after the bread/get some bread. "Он стоит за стеной" - He is standing behind the wall. Etc
They can, but the are not used interchangeably, they are used in different contexts. In my financial analysis I often write that buyers purchase this and that. But it's harder to imagine a mom saying to her kid - go purchase some ice cream. Yes she can say that, but does she say that? not often I would imagine.
Almost all synonyms exist for a reason, very few words are truly 100% interchangeable.
It's not an order in the sense of being impolite, especially if used with "please". It's no different to an English phrase like: "Pass the salt, please".
I suppose: "Do this, do that!" without any: "please" is a bit rude, or at least bossy. But there's nothing inherently rude about the imperative (in either language) that means you couldn't use it with friends. "Please buy, please give, please tell" etc.
It's an order or a request. You're indicating what you want somebody to do. It's not only used by army sergeants!
Talking about angry sergeants, there is a way in Russian to be rude or bossy, you can use infinitive instead of imperative. Instead of saying sit down - садитесь or stand up - встаньте, you can say Сидеть - to seat, Встать - to stand up. This type of ordering is used in military, prison, in court and with dogs in training. Some of our users in English course for Russian speakers claim that it is a normal way to speak like that in everyday life, but I believe they've been abused by their parents or managers (some angry parents indeed use this form and it is very abusive).
Actually, I don't think that "Pass the salt, please" is imperative at all, but a truncated version of English polite conditional, "Would you pass the salt, please."
The same thing probably applies in Russian - at least the intent is understood that the "imperative" is actually a polite request.
That could very well be; as someone else pointed out on another thread, the non-native ear can have trouble picking out subtleties that seem obvious to native speakers. Now I can just imagine what hicks we sounded like trying to pronounce their words (although I was told my pronunciation was very good; I was even mistaken for an interpreter a couple of times.)
In the UK, at least, "pudding" is often used as an informal generic term for "dessert" - any dessert - whether or not it's actually a pudding.
"Dessert" is more correct - as well as being the most obvious translation, when "десерт" is actually in the original. But it's still not uncommon to hear: "What's for pudding?", meaning: "What is the dessert?" I suppose it dates back to times when the dessert course usually was a pudding of some sort.
The Queen almost certainly wouldn't say it, but millions of ordinary people do.
"Must have been a Russian who learned "Brit" English" - nonsense
The sentences are written in Russian and then translated into English. This one is just an alternative translation, not even the main one. We must take into account that users of the course come not only from the US, but from other countries too (you should too remind yourself that not all English is the American English, from time to time).
Not always, the preposition is not enough, you need to understand the meaning.
на десерте means something is put on the surface of the dessert, a cherry or chocolate pieces, for instance.
на десерт means something is bought or prepared for the dessert, as a dessert. It's easier jut to remember this phrase as a whole.