"We placed the vase ONTO the table" (my emphasis) is considered wrong. Funny since this appears in the hover hints as "onto the table" for на стол. Also, if I understand it clearly, this sentence implies direction, not location, so "onto the table" is more apt than "on the table". Reported it.
I think "onto" is arguably correct here - but as a second definition of на, not as the better "on". However:
"Placed...onto" is just not natural English idiom (American English, that is). Idiomatically, it's not wrong, but not the better choice. I can't cite a rule for this conclusion, but essentially, "to place" includes the concept of moving an object to a particular location and leaving it there - the "to" part of the action is an implicit part of the verb "place", and using "place onto" is thus redundant.
It is true that translating на as "onto" instead of "on" helps understand why one uses Accusative instead of Prepositional case in such sentences ("onto" implies motion), but, once understood, better English idiom makes "on" the correct preposition to use with "to place".
I've been seeing "на стол" quite a bit throughout this course. Maybe it's explained somewhere and I haven't seen it, but why is it "на стол" instead of "на столе"? Sorry if this is a dumb question. I've been studying Russian for a long time and strangely I never came across this before.
Much like the preposition "в", you can use "на" to reflect whether something is happening whilst already being on the thing you're referring to, or whether the thing you're describing has (been) moved onto that thing.
If your sentence describes an action that happens entirely on something - you use the prepositional case. E.g. "Ваза стоит на столе".
If your sentence describes an action that doesn't originate on the thing you're referring to, but ends up on that thing - you use the accusative case. E.g. "Вазу поставили на стол".
Sure, it's basically the same thing. If you're familiar with Latin, it follows the same pattern with its preposition 'in': you use the accusative case to describe a motion from outside into something ('Eo in urbem' - 'I'm walking to (into) the city'); and you use the ablative case to describe an action/motion occurring in something ('Eo in urbe' - 'I'm walking in the city').
In Russian, that would be:
"Я шагаю в город" ('I'm walking to (into) the city') - answering the implicit question where to. Uses the accusative case.
"Я шагаю в городе" ('I'm walking in the city') - answering the implicit question where. Uses the prepositional case.
I thought I had sent a reply but it appears to have got lost. What I said was thank you so much and that my Latin was a very long time ago! Now if I may another question when going to somewhere is there any guide as to which you use. For example my guide says when using in the accusative form with verbs of motion идти в музей and then идти на площадь ? is this because the subtle maybe not so subtle difference is between the assumption that you will be in the museum but "on" (I don't like this use - we don't use it in English) on the square?
Historically, the choice between "в" and "на" is based on the idea of confined spaces - meaning that "в" is used for spaces with clear borders, whilst "на" is used for spaces with blurry borders - which is pretty similar to the way the English language distinguishes between 'in' and other prepositions. To an extent, it does indeed follow that the choice of preposition also reflects how much stuff there is above your head; but there are quite a few exceptions, so the choice sometimes seems almost arbitrary.
I'll try to systematise it here.
Russian uses "в" with:
Most buildings and parts of buildings.
в театр (but "на завод", "на почту")
в комнату (but "на кухню")
Non-open outdoors locations, countries, cities.
Russian uses на with:
Events and activities.
Geographic areas (implying natural, rather than political borders) - islands, peninsulas, mountain regions.
на Фарерских островах
на Аляске (but "в Сибири")
Open outdoors locations.
на улицу (but "в переулок")
Some of the exceptions I've outlined in the parentheses can be explained, to a degree. Places like почта, стадион, завод, вокзал aren't (or weren't originally) contained to a single building, and instead include/included surrounding buildings and structures as well - things like train tracks, stables, etc. That's why they came to be used with "на".
Some words can be used with either of the prepositions, depending on the meaning you're trying to convey:
Дети играют во дворе - 'Children are playing outside' (meaning an enclosed or at least somehow designated space outside the house, like a yard or a garden).
На дворе стоит туман - 'It's foggy outside' (not referring to any specific region outside the house).
It's not grammatically incorrect but it's a form that is not often used in normal speech. Without a specified time, "we have put/done/eaten/etc." is the confirmation of an action that was being expected. For example, "Did you all eat before you came today? Yes, we have eaten." "Was the command executed entirely? Yes, officer, we have completed the task." "Children, did you finish the table settings? Yes, we have put the vase on the table, like you asked." So without context, it's strange to use that form with this sentence.
I am still very much in the early stages of learning the difference between imperfective and perfective, but....
I could agree with a22brad22 much more easily if the verb were imperfective; it's not, though - it's perfective, implying that there was a goal or desired result, and that result has been accomplished. "have put" should be accepted, because it is a very likely translation of the perspective verb here.