「宿題をやらなかった。」means not only "I didn't do my homework",but also "I didn't have the intention to do my homework".And it also means "I'm saying just the fact that I didn't do my homework yesterday".So that words are used when you wanna say "I didn't do my homework,but I"ll do it today".
「しゅくだいをやりませんでした。」is polite version of 「宿題をやらなかった。」.
You aren't wrong that they could both be translated "Before going on a trip, I'm going to buy a ticket". But, there's a slight difference in context/nuance provided.
旅行の前にきっぷをかいます。really focuses on the action of buying a ticket. You
will simply buy a ticket before you go on the trip. You aren't
implying any sort of preparation.
None of these words can substitute for 準備する. They are not synonyms.
整う means for a bunch of things to come together to make a cohesive whole, or everything's in its right place. 準備が整った，夕食の用意が整った
I've never seen 設ける used to mean prepare, though. I did find 一席を設ける though, "to plan a party". But moukeru usually means to establish.
備える means to keep to do ...
from what I gathered so far (including the other answers), ningen could be translated into "sentient dweller of the Human world/reality plane) morally compatible with us". it seems to refer to the ascended conscience state, as opposed to an animal which is driven by its instincts.
Two other words to contrast with:
The word Hito would then refer to the ...
The「というように」in the second and third examples is hard to translate, but you could kind of imagine it as if it gave quotation marks to the previous statement, like「『夏には冷たい飲み物、冬には温かい飲み物』というように…」. In this sense, the literal meaning would still be akin to "As if to say, 'cold drinks in the summer, warm drinks in the winter', (...)". Still, it doesn't turn it into ...
Xというように would literally mean "in a way which says X". From which we can extrapolate:
分かったというように = in a way which says he understood = as if to say that he understood.
冬には温かい飲み物というように = in a way which says that it's warm drinks in winter = in a way which dictates it will be warm drinks in winter = in such a way that it will be warm drinks in winter.
気楽な corresponds to 気が楽 and describes feeling at ease or relaxed, a semi-literal translation of the latter might be "ease of mind".
"Easy" itself has several meanings in English, and "easy to drink" would not necessarily be interpreted as meaning the opposite of "technically difficult to drink".
In any case, translating 気楽なお酒 as an "easy drink" would be ...