It depends on the case and on wether it is an animate or an inanimate noun. In this case "лук" is in the accusative case and can either be singular or plural; furthermore, it's inanimate, that means that in the accusative case of both singular and plural, the noun stays the same as its nominative form (if it was animate, it would have been like its genitive form). Notice that this is valid only for masculine nouns.
I only slice onions which have already died. For more on this topic, see the movie "Notting Hill", esp. the episode about the fruitarian, Keziah
I haven't gotten to whichever modules teach the perfective/imperfect distinction, but have seen it in conjugation tables, and know enough to realize that perfective deals things which are completed and imperfective deals with on-going things. More comments on this distinction are welcome, including corrections to what I just said.
This is the first verb-pair I have encountered where the difference is simply one of pronunciation. All the others have added a syllable at the beginning or end, changed the spelling a bit, etc.
I don't think so. In English we'd say "Will you slice some onions?" or "Will you slice the onions." In the first case, there may be a bowl of onions and you are asked to slice some of them. In the second case, the onions to be sliced are already determined. Onion is a collective when you mean it as an ingredient, a substance or flavor, but when you mean specific onions, it is countable. So it's hard to imagine a situation where we would ask the question with just "onion."
I gather that this sentence, depending on context, could be either a real question "Is it really your desire to slice the onions?" or a very colloquial polite request to a friend or relation helping in the kitchen: "Please slice the onions." In that case I prefer "Would you like to slice the onions?" but "Do you want to slice the onions?' Is equally idiomatic.
'Do you want to chop the onions?' should also be accepted. Наре́зать is used for cutting into small pieces, when the pieces are of roughly equivalent shape, regardless of the shape.
To specify the shape, you use наре́зать ку́биками 'to cut into small cubes', наре́зать коле́чками 'to cut into small rings' (more formally, наре́зать ко́льцами 'to cut into rings'), наре́зать соло́мкой 'to cut into small straws'.
I don't think the difference between резать and нарезать is important here. Ре́зать and нареза́ть are imperfectives, наре́зать is perfective.
Ре́зать is more general-purpose. Наре́зать refers specifically to cutting into pieces of roughly the same shape, ре́зать refers to any kind of cutting. Basically, here's the difference between the verbs:
- to cut something into two halves or other well-defined parts, not neccessarily similar to each other = разреза́ть (imp.) / разре́зать (perf.) or ре́зать (imp.); e.g. this is what you do to make an A5 paper sheet out of A4 sheet;
- to cut something into a lot of small parts = нареза́ть (imp.) / наре́зать (perf.) or ре́зать (imp.); e.g. this is what you do to make confetti out of a paper sheet;
- to make partial cuts, that don't divide the object into parts = надреза́ть (imp.) / надре́зать (perf.), or ре́зать (imp.); e.g. this is what you do to make octopodes out of sausages.
Basically, ре́зать refers to all of this. It also has a perfective поре́зать which can be used in all those meanings, but this perfective form is pretty colloquial and generally sounds worse.