Would "I dag er torsdag" be considered wrong to say? I find that additional 'Det' rather confusing.
It would be wrong. The sentence requires a subject so we have to put "det" in there. (edited)
So, in English "today" would be a subject. In the literal translation "In day", "day" isnt the subject?
No, you need a subject in the English equivalent as well. You would say "It is thursday today." The "it" is the subject just like "det" is the subject in Norwegian. You'd also say "It rains", not "Rains." :)
"Today" is a noun as well, though. For example: "Today is the day." "Today is a day of rest." In the sentence "Today is Thursday", "Today" is the subject, "is" is the verb, and "Thursday" is the direct object, so it would be a correct sentence technically. Admittedly, it does sound weird without the direct object, so maybe I'm wrong.
Why does the "det" come after the "er" instead of before? And must it always be in this order, or is it okay to say "i dag det er torsdag" as well?
In Norwegian the verb is always in the second place, except when you ask a question. So no, it is not okay. You can say "det er torsdag i dag", though.
Relative to whatever makes up the first place. This can be both a single word, a prepositional phrase or a clause (and the list goes on...), so it's a bit tricky to get right initially, but in this case it's the adverbial "i dag".
For more information, I'd recommend you check out this helpful post on word order written by one of the Swedish mods (1.4 does not apply), and you can also google the "V2 rule".
I'm still confused as to why "det" comes after "er". Any hints? Why is it "I dag er det torsdag" and not "I dag det er torsdag"?
The verb has to be in the second place in the sentence. In the first place here you have "i dag" so then "er" comes second. If you'd move "i dag" to the end of the sentence, you would write "det er torsdag". So "det" would take the 1st place and, again, the verb "er" would take a 2nd.
Which is more natural for Norwegians "Det er torsdag i dag" or "I dag er det torsdag"?
Never mind Norwegian - I just forgot how to write "Thursday" XD I think I will never get how people can easily switch between languages...
I have seen that some norwegians write idag in one word, does it have another meaning than i dag or are they just too lazy to seperate the two words?
It's considered a typo in Bokmål, but would be understood as having the same meaning.
I don't necessarily think it's laziness, but rather them not knowing better. It's one of the more common mistakes to see in writing, and probably has to do with 'i dag' often sounding more like one word when pronounced.
You will see it in older texts as well, and I believe it's still considered correct in Riksmål.
Today are it Thursday. The literal translation. No wonder English speakers can't make sense of this. I've never heard a single Norwegian say this this way, or type it. But I've only lived there, what do I know, I don't speak it fluently yet, so maybe they do say that...