I noticed that it destroys trees on spread, but my miners, belts, and power poles are unaffected. I've tried placing buildings on the ore but nothing happens, or at least that's the case when it's not spreading.

Does tiberium have the capacity to destroy my base if it expands that far? It's very slow to expand so that's not really a cause for concern, but I'm just wondering what's the point of controlling tiberium spread aside from protecting myself from radiation damage.

Well, I had some solar panels and radars scattered throughout the map and one group was pretty close to tiberium so it eventually got grown onto and damaged. So I'm guessing miners, belts, power poles, and perhaps pipes are all unaffected by tiberium.