I came across these broadcasting vans recently in London.

The antenna that's deployed I think is a Vislink Advent uplink antenna, similar to this model, designed to transmit to satellites for television broadcasting.

The antenna wasn't pointing directly at the building on the right, but close enough (the cylindrical beam from the antenna would have passed approximately 2-3 meters from the front edge of the building) to make me wonder about radiofrequency exposure to the building.

My questions are:

1. How much peripheral scatter occurs with these antennas?
2. Would transmitting in this configuration raise any RF exposure concerns (a) to the building, (b) to the pavement to the right?
3. Hypothetically, what would the RF exposure be from direct exposure to the beam?

How much peripheral scatter occurs with these antennas?

Pretty much none. These are highly directive antennas; a good approximation[citation needed] for the opening angle of the beam is

$$\theta [°] = \frac{70 \lambda}{d}$$

say this is 10 GHz system, so $$\\lambda = 0.03\text{ m}\$$, and from that picture $d=1.50\text{ m}$, so the opening angle would amount to ca. 1.4°.

Say that roof edge is 20m away, then with a bit of sine you end up with a beam widening of maybe 48cm.

Also, the transmit power probably isn't that large.

Would transmitting in this configuration raise any RF exposure concerns (a) to the building,

nope, as calculated before,

(b) to the pavement to the right?

Even less so, since that's far from any direction of the beam.

Hypothetically, what would the RF exposure be from direct exposure to the beam?

Hypothetically, the RF power times actual antenna gain divided by the free space path loss.

Since none of these three are known, can't give you a number, but I doubt it'll be nearly as relevant as the phone in your pocket, unless you're hovering a couple meters away from the dish in the main beam.