some people hot glue onto slate, some use screws in slate/granite, some use fishing line to a rock. Sometimes the air works its way out of it and sinks on it's own after being submerged. But don't count on that, I forcibly submerged mine for 3 months and it didn't change a thing. It still releases air bubbles even 2 years later.
As far as that driftwood, if it's not you could probably make it safe. Simply by pouring boiling water on it a few times to kill any microbes that are on it.
After that, it may leech a little, or a lot, or no tannins into your water making it darker, and may lower ph.