Is this SD card compatible with rooting my nook tablet?
Also once I install the android os, if I take the sd card out, will my nook tablet revert to nook os?
The link nis for a full size sd card. It will not fit into any Nook. You need a micro sd.
Rooting in itself doesn't mean you install any alternative OS.
You can install OS internally or run it from sd-card. If you install internally that's what the NT will run, card in or out.
If you run it from sd the NT will boot into BN OS when the sd card is out.