Yes, sort of. It isn't wrong to say Vi har en rast nu but there's a tiny difference in meaning and the one without an article is the most useful version of the sentence. Adding en makes it a little more about having an individual break while ha rast is more like an activity, almost as if it were a verb in its own right. The stress is on rast too, just like in particle verbs.
In English you can have a rest or take a break, you cannot have a break or take a rest.
Saying "we are having a break now" would cost you points for grammar in English class in middle school.
It's cultural. Under the Anglo-Saxon economic model breaks are still not something everyone is granted, nevermind entitled to. You don't always just get to have breaks, you have to take them.
'rest' is cognate with the Swedish 'rast', but does not mean exactly the same thing. I believe it's the standard way in Swedish of expressing a free period in a school schedule when classes are not in session, but I don't know for certain beyond that how it may be used. 'paus' seems to be a close synonym in Swedish, and seems based on a bit of looking to be the more common word for a break outside of the school sense that's used here.
FWIW it's also not the same thing as what 'recess' means in most places other than American primary schools. The use of 'recess' there is in the sense that classes are not in session (they're in recess). I'm not quite sure what the closest word in Swedish would be, but I think it's 'uppehåll' or possibly 'lov'.
In a more general sense I wouldn't say that break and rest necessarily imply the same things in English. During a break you stop doing something, but nothing is implied about what you are doing instead. However, rest implies that you are in fact resting/doing something which will allow you to recouperate.
I think I agree with you both. Having a rest is more ambiguous in meaning, so perhaps it's better that it's not accepted. Unless of course rast is only ever used in reference to a scheduled break. In other situations I'd say that having a break is synonymous with having a rest.
"Break" (rast) was always called "playtime" when I was growing up in Scotland in the 1960-70s - not just at primary school but also at secondary. It was the time to get out of the class and have fun with your pals. I remember using the term "playtime" when I was at university too though that was probably just me :) Everytime I see or here the word "rast" here in Sweden, I think "yippee - playtime". Not suggesting that "playtime" should be accepted as a translation here - although we do use it in our bilingual home here.