Well, let's try to explain what each time preposition means then. I warn you it might be confusing or not accurate 100%, still it's worth a shot.

За - For me it indicates the continuity of the respected action and what I mean is that it gives me a notion that the respected action is stretched during the time stamp of the given time.

За три дня я выучил/выучу/учу 40 слов - It kind of means that you constantly learn withing those three days.

На - It's kind of for how long the action is active in the time you provide.

Его посадили (посадят/садят) на 2 года - He's been charged 2 years in prison
Статуя рассчитана на 40 лет - The statue is considered to last for 40 years.

Через - this just shows what will/does/did happen after the period of time you provided

Через десять минут будет готов завтрак - The breakfast will be fixed in 10 minutes
Он закончил говорить через десять минут - He stopped talking after 10 minutes
Я иду в школу через два дня - I'll go to school in two days

Нет предлога - Well, that's kind of tricky to explain this one. Well, it's usually used to say for how long the action is/was/will be active

Он хромал десять дней - He was limping for 10 days
Я думал пять минут - I was/have been thinking for 5 minutes
Я думаю 5 минут - I am/have been thinking for 5 minutes

Well, I don't think it's gonna help but at least I tried