Is there a place right at the station to just pick someone up? And perhaps wait 20 minutes for them?

Yes parking is very scarce right next to station. I had to pay for parking before, parking garage is right next to train station.

Never had an issue there for that short a time. I travel through twice a month.

Maybe at a few minutes walk across the street

Very limited free parking, just across the street in front of station. Get there early.