Meet the Ariane EAP (Étage d'Accélération à Poudre, "Solid Booster Stage"):
what are the (presumably eight) circular spots on the external nozzle-like protrusions at the bottom of each of the (presumably solid rocket) boosters on either side of the main engine?
They are the business ends of the fusées d'éloignement, or separation motors, which push the SRBs away from the core after they burn out. There are four, not 8, at the bottom of the booster, and four more at the top -- all pointed generally inboard to drive the SRB casing away, but not so directly inboard as to impinge exhaust plumes on the core.
what does one call these nozzle-like protrusions when one has one's space words handy?
Those are the jupes arrière, or aft (nozzle) skirts. The rocket nozzles themselves extend beyond the skirts, through holes in the structure.
does this launch vehicle simply sit on these nozzle-like protrusions?
I believe that's correct - the entire weight of the launcher is resting on those nice flat plates.
Is there a lock down mechanism somewhere?
I would have thought so, but @Hobbes' answer suggests not.
Your still image (from T+0:04) is from a remarkably high-quality video, but it unfortunately cuts away from that camera just before the EAPs fire at T+0:06 (but not before you can see a lovely blue hydrogen-combustion shock formation in the Vulcain's plume!). Later in the video you can see the booster separation, but the sep motors aren't really visible at that distance -- the residual plume from the boosters is much brighter.