Orangeyellowgreen, that is what I suspected.
I consider myself lucky to have had the opportunity to learn grammar through Irish in school in Ireland, along with Irish itself. It is perhaps one of the more complex European languages, grammar-wise, with changes of ending in verb tense and person being the least of your worries.
I am Irish, not American.
I too have had discussions on MN about English grammar, and you are right, there is a lot of rudeness here. Never before have I come across such bald statements as 'repulsive' and 'ugly', referring to a mere word, or statements like, 'So you might use it - if you were a dick - when talking about something "we got" but not "I got".'
'I did get' is not correct and if the Danish friend uses it all the time then someone should do him a favour and correct him. Maybe I should judge his friends and acquaintances for being so remiss. I may be misguided to be so judgey, but I am not thick.
You shouldn't struggle with 'gotten' based on verb endings in Dutch or German. It's an English word. The languages parted company quite a while ago. American English does not use 'gotten' for any more tenses than it uses broken, written, forgotten, driven, arisen, beaten, chosen, eaten, stolen, woven, forbidden, forgiven, forsaken, frozen, woken, taken, spoken, shaken, proven, hidden, fallen, etc., all past participles.
All three perfect tenses use a form of 'to have' as an auxiliary --
'Have' or 'has' + past participle of the given verb is the formula for the present perfect tense.
'Had' + past participle is the formula for the past perfect tense.
For the future perfect, 'Will' + 'have' + past participle is the formula.
Along with forms of the auxiliary verb 'to have', can, could, may, might, must, ought to, shall, should, will, and would can be used.
These are the only ways 'gotten' is used in American English or any other form of English. These are also the only ways all the other -en ending irregular verb past participles (partial list ^^) are used in any form of English.
Past, present and future perfect continuous do not use the form 'gotten'. Past, present and future continuous do not use the form, and neither do present, past or future.
Conjugation
Maybe I am being picky (or wrong) here, but you seem to have mixed up the verb 'to get' and the verb 'to have' in your Dutch language example.
'Scale of misapprehension' means 'extent of misapprehension'. Meaning there is lots of it.