Mike is living in Cairo, should be accepted because lives and is living are the same in my opinion. An Arabic expert please clarify.
On Duolingo's level, yeah they are the same.
If I want to take a step a bit deeper into the language and its correlation to English, then yeah they are different (but I don't think Duolingo is paying much attention to that correlation anyway).
You see, the word (living) is in act a noun and not a verb (and because of this we use "is" before it, and "is" is the main verb in the sentence). So, as a comparison, the sentences Mike lives and Mike is living do have their counterpart in Arabic as well:
- Mike lives in Cairo: مايك يعيش في القاهرة
- Mike is living in Cairo: مايك ساكن في القاهرة
In the second sentence, I've used the subject-noun derived from the verb سكن (sakana: to settle) rather than the verb عاش (3áša: to live) just because it is the usual way to say it (not saying impossible but this is how it is commonly said).
Subject-nouns (Arabic: اسم الفاعل Ism-ul-fá3il) is almost the equivalent of -ING nouns in English, and there is a somewhat regular and systematic way to derive those from verbs.
Notice I'm not telling you this to show that your answer is wrong; I'm sure Duolingo Arabic Course creators didn't put much thought into this issue. But I'm stating this in hope to expand your linguistic knowledge in general, away from Duolingo, specially when it comes to translating between 2 languages like Arabic and English.