Yes. Instead say: I've been here since January. (I've = I have)

Yes, it is wrong. When I meet a new student, they often ask "How long are you here in Slovakia?" I clarify by asking, "Do you mean, 'When did I arrive here?' How long from then, to now?" The answer is usually yes, so then I'm able to explain how present perfect ("I have been here") is necessary, and how present simple ("I am here") is a different question. When you want to know the length of a person's stay up to now, you use "How long have you been here?" The answer may be "I've been here since January." Seeing words like "since" tell you that you need present perfect. It's how we connect the past to the present. You can also answer with "I've been here for [time period]." When you want to know how long a person plans to stay in total, you use present simple. "How long are you here?" "I'm here for one year." This doesn't change at all. If you arrived in January and asked the question in March, August and then November, then the answer is still "I'm here for one year." Your total plan.