Sandman mystery shots (1 Viewer)

[that subject field was supposed to say “San Fran”; autocorrection occurred but I can’t edit]

Here are two fluke photos from a brief bird watching hike to Buenaventura’s vista park in urban San Fran.

The first pic is a hawk (on the right) being harassed by a crow. This went on for some time just above the treetops and all I got was this shot, alas. Which hawk I wonder?

The second shot is a crop of what was a pic of a scrub jay that was photobombed by this character. I presume some sort of woodpecker, but which?

Pics from 2 june 2019.

Thanks for any insight
E2

Violet-green Swallow for the second.

Ok wow.
Thanks
(I was just reading your thread on Euplectes)

I don’t see the same light gray collar visible in my shot when I search “violet green swallow in flight”...

I had other shots of swallows that day which I deemed un-identifiable... but here they are anyway!
(Included here is the full frame /lower res version of that pic of scrubjay with the bird in question)

Thanks
E2

Inicidentally there was a Lewis’s WP reported on eBird at that park ten days prior, which is how I ended up going that direction (along with a dose of ‘birders optimism’)

All swallows look like Violet-green to me.