In the video, Amy demonstrates picking up stitches, but you can't really see where the new strand of yarn is anchored. should i just hold it tight w/ one hand and then weave the end in later?
Yes, just leave a few inches and start picking up the stitches, it won't come loose.
If you do find it fiddly you could attach it with a safety pin until you have done several rows/rounds
I saw the Yarn Harlot herself on an episode of Knitty Gritty, and she was picking up stitches just with the needle, no new thread at all. Are there some situations where it's better to that than to do pick up a new thread of yarn? :??