1. The yellowish color is from tannins. These are harmless (and in some cases beneficial) organic acids. Your wood may leach tannins for weeks or months. You can hasten tannin removal by boiling the wood. You can reduce the yellow appearance in your tank with increased water change size/frequency and activated carbon.
2. The fuzzy growth is a harmless fungus. It will disappear in a few weeks as the bacterial biofilm becomes established. Scrubbing it off will renew the cycle, so it's better to leave it alone or to gently remove the outer portions only, leaving the wood itself untouched.
3. It will take a while for the wood to become waterlogged, and some pieces never get there. For a more permanent solution than piling rocks on, try bolting the wood to a piece of slate. This acts as a weight, and can also be covered in substrate for additional anchoring.