I would personally think the above sentence would be more 'want' than 'need'. My hunch is that मुझे आरम की ज़रूरत है would be 'I need rest', but I'm not mother tongue.
Zeebo7 is right. मुझे आराम चाहिए can translate to both 'need' and 'want'. But if you want to strictly denote 'need', use ज़रुरत है.
Same question. Would that be a correct translation, or would it have to be "Mein aaram karna chahie."?
duoling get very anal and want you to say "need" even though चाहिए can also be translated as want.