I noticed that after the cycle, some water, very little, remains at the bottom of the chamber. I removed the plastic dome at the bottom and checked the pit under it; the pit was full of water. The hose connects to the garbage disposal pipe, no air cap. I disconnected it there and was able to blow the air through the pipe with my throat; heard some bubbling where the air went through that water. Is it normal for the water to stay in the pit?

Yes, this was the first thing I checked, and it's ok. Actually, that part, with the filter frame (position 543 at the picture below) is somewhat raised above the bottom of the main chamber, and the water that stays at the bottom of the chamber is below that level. And the pit is even lower.

By the pit I mean where position 508 at the picture is submerged, which is under the plastic dome position 506. Or maybe the correct term is "sump".