Why can't it be "ret moderne"?
I'm native danish and I can tell you that he is pronouncing 'moderne' totally wrong. It is not moderne with a flat d, it is moDerne with a hard d.
Does the word "veldig" exist in Danish? I'm having a hard time avoiding that word and instead using "meget" since I tried learning Norwegian previously.
It does, we just spell it "vældig".
Can it be "meget modernt"?
No, "moderne" is an adjective that ends in an "e" so remains the same whether it's neuter, common or plural
Would "helt moderne" be wrong?