Why does the spawn have the spacecraft-shell too? That's a very good question. Here's an answer I've fathomed up:
The shell is a part of the body just as much as a turtle's shell is part of it's. When the shell of adult Lavos is broken in Trigger, we fight a large tentacled being that seems to be a part of the same mass the shell is, because it has no lower half, just a large fused hunk of flesh to the nearby ground/wall. This might be the real "body" of Lavos.
As for the humanoid looking Lavos and the bits, I like to think of them not as essentially physical entities, but rather the conscience of Lavos. The "dream" of Lavos that is a counter to the "dream" of the planet. The entire final battle is fought in the subconscious of Lavos, and the pictures of many eras and locations you've crossed during the adventure are those collected from Crono and crew's minds synchronizing and duking it out with that of Lavos.