There is no way to close tickets from the user's side. Currently, there's only one active mod, so it could take anywhere from a week to years, depending on how many tickets are in the queue. I'd advise you to keep bumping the tickets you want to be addressed and comment "the issue has since been resolved" or something similar on the resolved ticket.
So i've submitted 3 tickets (only one has been resolved) and its been a few months since the oldest one was submitted with 0 progress or updates, and the one that HAS been resolved is still open. is there any way to close a ticket thats been resolved? how long does it typically take before toyhouse staff gets back to you about tickets?