Surface cache only handles 2+ bounce (assuming that recursive reflections are disabled). So first we trace a bunch of rays from pixels. Ray which don’t hit any geometry will sample the skylight directly. Rays which hit something will lookup surface cache where we cache the rest of the ray path after the 1st bounce. Similar surface cache is what you see in reflections.
Certainly placing light sources like sunlight isn’t recommended, as Lumen won’t be able to discover reliably that single very bright pixel. As for the distant stuff - as long as it doesn’t need correct parallax it should work fine, and likely better than not having it all in GI or reflections.
I never saw anything like that before. Is this Lumen reflection issue or something with translucent sorting? Like does it happen when you disable Lumen reflections? Do you have some repro?
HDRI places a big mesh with HDRI as a texture on it. Sometimes that mesh has correct surface cache coverage, sometimes not. You can check it in Lumen Overview whether Lumen sees the same skybox as you expect. On the other hand placing that cubemap inside the skylight will always work, as it’s just a cubemap which will be sampled on any ray miss.