Can this also mean "I'll have an orange" in the same sense as "I'll take a coffee"?
Can I use this also to order something at a restaurant or there's a better way to say it?
Can tar also be using like 'can I have?' e.g. Tar jeg en applesin? (Would this be 'Can I take an apple?'
You could say: "Kan jeg ta en appelsin?", but it is more common (and sounds more polite, I would say) to use what Wylga says, "Kan jeg få en appelsin?". "Tar jeg en appelsin" would mean something like "Am I taking an orange?". And if you did grab one just then you would know, right?
I think you would rather use 'kan jeg få' in that case, which translates to 'can I get'. So it would be 'kan jeg få en applesin?' But I don't know if the other one is acceptable too.