Is "I am living with my uncle this month" correct?

Why

The friend's assumption comes from thinking of the continuous tense purely through its most common use — describing something happening this exact second, like "I am eating right now". But the continuous tense's real job is broader: marking something as TEMPORARY, in contrast to something permanent or habitual, and "temporary" can genuinely stretch across weeks or months, not just seconds. "I live with my parents" (simple present) describes a permanent, ongoing arrangement, while "I am living with my uncle this month" (continuous) signals a known, temporary situation that will end — Kartik really is only there for a month, and the continuous tense is exactly the tool for flagging that temporariness. Test: compare "I work at a bakery" (a permanent job, simple present) with "I am working at a bakery this summer" (a temporary summer job, continuous) — both are perfectly correct English, and the tense itself is what signals permanent versus temporary. No, Kartik is right: the continuous tense marks something as temporary, and temporary can mean a month just as validly as it can mean this exact second.