Regarding the pergola on the opposite side of the street, what's the building indicated by the red arrow? It's not the Post Office building.

Sean, Charles Collins has already in this thread identified the building you are asking about as part of the loading infrastructure at the Union Station. I’m belatedly adding some info related to the photo you posted.
I had a chance to visit Dealey Plaza recently. Although the Bowers Tower was not on my agenda I did make video of the Fence-Shelter gap from ground level. I slowly side-walked from the west corner to the east corner. Attached is a frame taken at approximately half the width of the tower that would be under the center window facing south.
I learned from this experiment that the south pergola’s shelter is not responsible for the smallish structure to the right of center in your posted photo. I made the mistake of using that structure as the west pergola shelter, which put my estimation of the photographer's location too far east. I recently found an aerial labeled as from 1968 that shows some structure about 14x14’ and about 50’ SW of the pergola’s west shelter.
https://www.historicaerials.com/location/32.74639398582965/-97.31540992856026/1963/20#I believe this structure is a shed. It does not show in 1972 or 1958 aerials. I also found2 an on-line (full?) frame version that was possibly the original. Your posted image from which we’ve been studying is cropped. The fuller frame version shows the camera at elevation. I believe that the photo fairly represents a view from Bowers’ tower.
I have only found one contemporaneous photo that shows the Union Station freight handling bridge. It is at upper-right frame as the last building to the west in the Volkland photo. This structure is gone in a 1979 aerial.
https://drive.google.com/file/d/1EYOQJcqOn5nymrOqkas6mugzDJCu0Ws_/view?usp=drive_linkhttps://drive.google.com/file/d/1xZeS_7URmL8Z3S25woO5nyobTUDTumt7/view?usp=drive_link