Is there a place to bring your lunch and eat like a food court

There's seating on the median of the street. Small round tables, mostly under tree shade. Closer to the southern end there seems to be fewer homeless people /panhandling

Yes

Wouldn't call it a food court, but there's some outdoor seating that's open to the public.

There is outdoor seating in the median of the 16th Street Mall where you can sit and eat.