Do I have to choose a Pantone black, or can I just use 100% K?
Yes, Black belongs to the set of 14 Pantone Basic colors from which all other PMS colors are mixed:
If you're using Illustrator, you can find it as a swatch in the PMS color book swatch library
Or in the Color Libraries in Photoshop:
There are other "Blacks" available (Black 2, Black 3, Black 4, Black 5, Black 6, Black 7) but they are all tinted with some other color (yellow, green, orange, red, blue, and silver respectively). Just go with the base black if you want the "blackest" black available.
Yes, black counts as a color. However, you can use 100%k if you'd like.
I've never called out a specific Pantone Black unless there was a reason I wanted that Pantone black.
As @JohnB points out, Pantone makes a number of blacks, if you aren't looking for one of those (tinted) blacks, then using 100K is just fine.