"I should go now."
Translation:अब मुझे जाना चाहिए।
Does "अब" always have to go before "मुझे"? I feel like you could switch the order of those two words and not change the meaning of the sentence.
Your are right. You can say मुझे अब जाना चाहिए। But the emphasis sounds different to me. The given answer just means that your are now saying you have to go. Putting अब next to जाना sounds to me like you are saying you have to go now (immediately, emphasis on "now").
चाहिए means 'want to' when used with nouns, but 'should' when used with verbs. The translation given is correct. "I want to go now" would (I think) translate as अब मैं जाना चाहता हूँ (चाहना can be used with both nouns and verbs to mean 'want').