When referring to time, i means for (the duration of). It is very confusing, I know.
Den var bortglömd i årtionden. / Under årtionden var den bortglömd. (It was forgotten for decades.)
Christian Dior var den ledande modeskaparen i årtionden. / Under årtionden var Christian Dior den ledande modeskaparen. (Christian Dior was the leading fashion designer for decades.)
Notice that I use under årtionden to start sentences, not when for decades appeares in the middle of sentences. I don´t know why I do this, but it is how I use my native language.
As far as I understand, 'på' is used for seasons and days. 'i' is used for months. Eg: på sommer, på tolsdag, i juni.
You have a few typos there: på sommaren (also, it needs to be definite in Swedish) and på torsdag. Otherwise you're right.
Because "Årtionde" is an Ett word, and it ends on a vowel, so the plural indefinite is "Årtionden".