I don't get 'got.' 'I have got object' as a correct English translation seems redundant and we have not covered the perfect tense if it even exists in Danish.
So 'Jeg' is not capitalized mid-sentence but it is at the beginning of a sentence. Is that correct?
It is. English is the only language I know which uses a capital letter for the first person (I). It is much more common to capitalise the courtesy forms (English "you" when addressing a stranger): it is done in Spanish (I see you're studying Spanish so you will find Usted (formal you) with capital 'U' but also in Italian and German. None of these languages capitalise the first person.
Why does the e that comes between the k and n get dropped when making the plural of this word? Doesn't seem to fit with any of the rules that I've learned to now...
The translation into English is poor. "I have got plates" is redundant in English. Your problem here is "have got".