Grammatically: accusative and dative are OBJECT cases. They create a feeling of an ---> arrow directed at them. They are like parts of a verb: "сесть-на-пол" instrumental and locative/prepositional are ADVERBIAL case. They are more disattached from the verb: they describe "how" or "where" was it done rather than "what". "на полу", "на диване" do not create a feeling of an "arrow". They create a feeling of a space: {........} within which you can pick a position. Maybe because of this it is less common (but possible) to say: "сел на стуле" (isntead of "сел на стул") but common to say "сел на диване" (alongside with more common "сел на диван"). Because диван is more like a space... And "chair" is less like "space". Such an adverbial can mean one of two things: 1) the whole action took place at the table. You were there initially. [I sat down] happened [at the table]. 2) your resulting position is somewhere at the table. [I sat down] and then [I'm at the table] ("я сел за стол" would then look like [I sat-down-at-the-table].

То есть, вы можете использовать оба выражения. Но в них есть небольшая разница. Примеры: 1. You're so tired, that your feet can't carry your weight. To your surprise you sit down right where you were standing, on the floor: Я сел на пол. 2. You and your friend are choosing where to sit down. 2 options: on the floor, and on the table. Your freind chooses the table. You choose the floor: Я сел на пол. (just a common way to say it) Я сел на полу. (more emphazis on that you were Choosing A Place to sit) Any of these (even "Я сел на пол, а он на столе"). 3. You're already lying on the floor. Then you sit UP. Я сел на полу.

Я ходил в школу в Москве. В Москве я ходил в школу. Что ты делал в Москве? В школу ходил. What you did? "went to school". Where going-to-school happened? In Moscow. Я ходил в школу в Москву. What you did? "Went to school to Moscow" Where did you do that? I don't know, but apparently your home was outside of Moscow. "в Москве", "за столом", "на улице" - место действия. ("в" и "на" и предложный, "за", "под" и творительный) "В Москву", "за стол", "на улицу" - это часть действия. ("в", "на", "за", "под" и винительный) Вы можете трактовать "ходить-в-Москву" как цельный глагол, описывающий движение: [снаружи]---->[внутрь]. Поэтому: "Я сел за стол" - I moved from "standind" to "sitting at the table". "Я сел за столом" - I sat down. The place where I did that was "at the table". This one is similar to: "Я расположился за столом" I placed myself at the table. "Расположился" is not a verb of movement. It means "occupied a place". So only "за столом".

Бежал (за кем?) за мной. Отвечает на вопрос "кем?" - творительный падеж. Я сел (за что?) за стол. Отвечает на вопрос "что?" - винительный падеж.