The answer to this question would vary, based on which country and which Hawzah institute you will to apply to. The age limit would depend on individual cases, and educational history. As for costs, there is usually no costs for joining the Hawzah.
For the holy city of Qom, the administrative body for non-Iranian students is Al-Mustafa International University. Their website is:
You are able to read information there.
Also, for general information and various options for Hawzah studies, I have a Facebook page that might be useful to visit:
With prayers for your success.