1: Congrats on your first cut-out...they don't get any easier from here, but you get less nervous...so they go a little smoother
2: That was a LARGE hive in the video...not huge; my 1st was about that size..built into the subfloor of a mobile home (don't think I'll ever tackle one of those again), my most recent cut-out was bigger than that, built into a wall (around water pipes), and hot Hot HOT HOT!!! (even before I started cutting down the siding with a circular saw). They stayed hot when I got them home too...right up until they absconded in true AHB fashion (which, from the size of the hive, my location, their temperament, and the absconding, I'm about 98% sure they were).
3: As far as bee vacs go, I'm sure they're quite useful, but I haven't had much luck with 'em...too fiddly trying to get just the right suction; I just cut the combs out, splice some brood into a couple frames, then try to scoop as many mounds of bees into the hive boxes as possible, hoping to get the queen so the rest will follow her in. (BTW: comb filled with honey from cut-outs goes in the TRASH; I've only EVER done one cut-out where I was pretty sure no pesticides had been used on the bees, the risk of neurotoxin poisoning from bugspray in the honey just isn't worth it).
4: If you go back to the rental house tomorrow, you'll prob. find a nice cluster of bees hanging somewhere near the remnants of the old combs...if you put a box/bucket under them & simply touch near the top of the cluster with your hand/bee brush, they'll likely drop nicely into the container so you can take 'em home and rejoin them with the rest of their hive.
Front & back halves of the hive from my 1st cut-out
A nice cluster of bees (actually this one's from an afterswarm that moved in 2 days after a cut-out)