1: Yes in Terragen 2, but no in Terragen 3. In Terragen 3 we decoupled GI prepass detail from main render detail. That's why it used to be called "relative detail" in TG2 and is now just called "GI cache detail".
2: It will not cause problems. Rendering will just use the cache as it is. You can generate a cache at higher or lower detail, or at higher or lower resolution. You can potentially use this for some functional purposes, although in practice simply adjusting the GI Cache Detail setting is generally easier and able to achieve similar goals.
3: The GI generation will be based on the cache you generate, regardless of your main render Detail setting. But it will be applied to the more limited detail of the render if you reduce main render Detail, so the results won't necessarily be better. Of course generating a higher quality GI cache takes longer anyway. But since the settings are now decoupled, you are free to use lower main detail with higher GI cache detail if you want.
As I understand the GI cache it's it's kind of the opposite of what you stated above: the GI cache *is* sampling lighting/color, and while it does store some geometry info about the position and normal of each sample, it is not storing geometry per se. Matt may chime in again with better info.

- Oshyan