Earth

==== So there are various implied connections between D&D settings and Earth. Is it implied that various Pantheons with real-world analogues (Finnish/Egyptian/Greek/etc.) got their start on Earth, or did they likely have their own worlds on the prime distinct from our own? ====

We know that the Pharaonic pantheon were worshiped on Earth at some point, but given their nature and power and the nature and lack of power of the world of Earth, it's likely that each of the major pantheons had their own home sphere and world. I've done some tentative sketch-ups of those worlds, but not much.

Do people who know of Earth (like Elminster) refer to it as such? Seems it could be easy to confuse it with the plane.
Primes, even well-traveled Prime wizards, refer to the Elemental Plane by its full name. Only planars and natives call that plane "Earth." People who know of the world of Earth know it by that name and may have other names for it as well.

For that matter, how many people know of Earth, besides those who live on it?
Very very few.

On Toril for instance, could an apprentice wizard learn of it in a "compendium of worlds"-type book at the wizard school library?
Not likely. Between the flood of Invaders From Space, the Shou Lung spelljammer fleet, non-infrequent contact with the other worlds of the Radiant Triangle and the fact that Toril has many major space trade ports, spelljammer-based world-to-world contact is much more documented than travels to another world's alternate Prime equivalent. Any such compendium would document worlds like Krynn and Oerth, but Earth is not in the cards.

Would such knowledge be held by higher-level and higher-status people, like archmages? Or would it be known by only a small few - Elminster and Mystra, obviously, perhaps one or two others?
Earth's not of interest to many people, being, as I said, a world on an alternate Prime without native magic. On Toril, the only people likely to know about Earth are those who have had it mentioned to them by Elminster and some rare few who might have journeyed there themeselves at some point or communicated on the subject of alternate Primes with Mordenkainen or Dalamar. So, next to nobody.

The reason you're not finding Solspace on the map is because it doesn't exist; Earth is an alternate Prime with a different cosmology.

==== Is Earth the source of the original Mulhulorandi immigrants, or was that just another world where the Egyptian pantheon was also big? If it was the former, than Earth may get a mention in the history books. ==== Earth is the source of the original slaves who became the Mulan people, the ancestors of Unther and Mulhorand. However, the Imaskari likely didn't record the name of the world they came from, if they even knew it existed, and the Mulan people wouldn't have known at that level of their cultural existence that they were brought from an alternate Prime or what its name was, nor have they demonstrated a serious interest in their travelly past. Given that a span of nearly 500 years exists between when the portals were opened and when the Imaskari recorded their arcane lore, chances are pretty good that mentions of Earth are nonexistent.

If Earth is an alternate Prime, how were these Wizards getting thet before the recent expansion of the Plane of Shadows?
Those travels occurred before the cosmological shift, and there are a lot of different and bizarre magical interactions and constructs that can conceivably reach alternate Primes. We just don't have them enumerated.