Yes I did exactly this a few weeks ago. The discovery pass is good for the day parking, and you need to pay for "unattended overnight vehicle" with a regular state parks envelope, which is $10/night and available at the launch. There is plenty of truck and trailer parking right there at the launch.
Yes you can leave vehicle and trailer. There is an additional charge, though. I believe it is $10 per night
Looks like there are facilities for this, but not sure of permit process
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