Are the there open track times where amateurs can bring in their own car/bike to see what 1/4 mile times they can get?

Yes but it depends on the events they are holding. Your best bet is to call the track and see what they have available.

Most Saturdays you can even during some of the big events.Check online or call the track.

Contact the track they are helpful

You want to check the schedule for a test and tune event