We don't use the article 'a' before advice in english because it is an uncountable noun. 'A bit of good advice' or 'a piece of good advice' are fine, but 'a good advice' is not grammatically correct. It should just be 'do you want good advice' without the article.
It's not saying "an advice", it's saying "a piece". 'Piece' is not uncountable.
Yes, if you read my post, I said 'a piece of advice' is fine. I translated this as 'do you want good advice' and a box popped up which 'helpfully' told me that my grammar was incorrect and I had missed the article 'a' i.e. I should have written 'do you want a good advice'. I was merely saying that 'a good advice' is not correct (and duo should not be telling people that it is!). However, I reiterate, 'a good piece of advice' and 'a piece of good advice' are grammatically correct.
I'd say it doesn't. 'A good advice', as discussed above, is ungrammatical in English. But apart from that, the Danish 'vil' is past tense.