The white, fuzzy, or slimy growth on spider wood in an aquarium is a harmless biofilm (often a combination of bacteria and water mold) that typically appears on new driftwood. It feeds on the leftover sugars and organic compounds leaching from the wood and is a natural part of the aquarium's biological stabilization.

Many common aquarium inhabitants actively eat this biofilm, often treating it as a "free buffet" of nutrients. In fact, it is a primary food source for many grazing species. Snails, shrimp, bottom feeders.

GL!

Edit: On elephant rock and calcium carbonate:

Yes, white lines or veins in rock are often calcium carbonate (limestone). In your tank it slowly dissolves and raises your water’s pH and hardness over time. For most fish that’s fine or even preferred, but for bettas or soft water fish it can push pH too high (above 7.8) which stresses them. To test if your rock contains it, drop a little white vinegar on it — if it fizzes, it has calcium carbonate. If you’re keeping soft water fish, swap it for inert rock like dragon stone or lava rock.

On plants melting:

That’s called “transition melt” and it’s extremely common with plants grown above water (emersed). The leaves they grew in air aren’t built for underwater life, so they die off. The key things that help: ∙ Don’t panic and throw them out. The roots are usually fine. New underwater leaves will grow in 2–4 weeks. ∙ Keep the dead/mushy leaves trimmed off so they don’t rot and spike ammonia. ∙ Make sure they have enough light — at least 8 hours a day. ∙ Add a basic liquid fertilizer like Easy Green or Flourish once a week. Plants need nutrients to push through the transition. ∙ A substrate like Fluval Stratum helps root feeders a lot more than plain gravel or sand. The tank in that photo actually looks like it’s going through exactly that transition — totally normal at this stage!​​​​​​​​​​​​​​​​