What to ask a prospective supervisor regarding advertised PhD position?
I would like to know if my profile fits their requirements.

If I were you, I would not ask this. First of all, it's not really clear what you mean by &quot;requirements&quot; -- you have already indicated that you meet the published GPA and language requirements, so it's unlikely that there is anything else they could tell you. Second of all, it's not relevant to your possible connection with this specific professor. Third and finally, professors are generally busy and do not always respond to unsolicited mail; the chances they will respond are even lower if you ask vague and/or logistical questions.
Instead, assume you do fit the requirements, and instead focus on your interest in working in this professor's group. Talk briefly about your qualifications (e.g., research interests and research or classroom experience related to the professor's area), and simply ask if they have open positions in their lab. Keep it brief but indicate your interest and knowledgability about their research clearly.
If you successfully establish credibility and the professor likes what you say, and they have open positions, it's likely you have good chances of getting in (because the professor can vouch for you). Typically, the actual &quot;requirements&quot; are not so important and may not even be well-defined.

I would like to know what to specifically ask professor when I write a mail regarding the advertised position?

The best question to ask is already in your post:

Do you have any open positions or upcoming projects related to [topic of interest X] in your group?

It's clear and to-the-point, and assuming your email has indicated you are a strong candidate, it gives them a direct opportunity to express interest in having you as a student.