"I do not have black shoes."
Translation:У меня нет чёрных ботинок.
Обувь means "footwear" and is a collective noun (it is always singlar).
As for the rest...
- туфли are women's shoes and dress shoes that men wear
- ботинки are, strictly speaking, higher than туфли and cover your ankles. However, in speech we often call lower shoes for men "ботинки", even dress shoes. I think, it is especially true if we are talking of men's shoes that are more "practical" than shiny and elegant. In this course we usually consider ботинки and туфли interchangeable
- сапоги are "boots" and are even higher that that
I stongly object to the use of ботинки for shoes. 'Shoes' should be туфли and nothing else. I don't know what made you say, "in speech we often call lower shoes for men "ботинки", even dress shoes". Even if you do, that's not the way to say it in Russian as it is, at least, confusing. It's true that in sales people's jargon shoes for men are often referred to as "полуботинки" (literally, "half-boots"), but it's been a long time since I heard the word.
Обувь is a general footwear.. but other two are sinonimous in English, except for ботинки is a man's daily footwear and туфли is all-gender formal/party footwear.
As a Russian woman I strongly desagree with the notion that "ботинки" is a men's footwear. They are very much unisex.
Is there a particular reason why the "нет" can't be at the end of the translation?
It can. By putting нет in the end and using special intonation to emphasize у меня or черных (namely, by pronouncing the stresses syllables at a higher pitch) you can add something to the general meaning of the sentence: "Someone else might have black shoes, but I don't" or "I have shoes of other colors, but not black ones".
Should обувь always be singular? Why isn't у меня чёрных обувей accepted? Thank you for any answers :D
Обувь is a collective noun meaning "footwear". It has no plural form.
У меня нет чёрныХ башмакОВ. Башмак is either obsolete or used with a little bit of irony. The word has Turkic origin and is mostly used in fairy tales or to refer to medieval footwear, especially the one made of wood. The diminutive form башмачок (the plural башмачки) is usually used for girls' or children's shoes/boots.
Wiktionary lists two different declensions for ботинок. Тhe respective genitive plurals are listed as ботиник and ботинков, but ботиноков is not accepted for this exercise. Am I reading the Wiktionary entry incorrectly, or is the declension with ботинков simply archaic or non-standard?https://ru.wiktionary.org/wiki/ботинок
As a native Russian who lives in Russia, I assure you that the gen. pl. form «ботинок» is the only one that is used in the standard language.
As a non-native speaker, ботинков just sounds "off" to me for genitive plural.
У меня нет черных туфель. wasn't accepted.
By the way, even without not talking into account that "ботинки" are rather boots, I consider "shoes" quite to myself shoes. And you?