I'm designing a basement bathroom, and I'm having trouble routing the sink to the ejector pit. I plan to run my shower and toilet under the concrete to the basin's side inlet.

The sink, however, is on the other side of the bathroom, and I wanted to run it to the pit through the surrounding wall, since it's high enough off the ground. This will save me having to bust a trench all the way to the sink. However, it'll require 2x90degree bends in the horiz/downsloping drain before it hits the pit Two questions:

1) Is it ok to have multiple bends in the horizontal drain line from the sink?
2) Can I enter the pit through the 2" vent inlet in the lid? That is, can I put a tee on the vent outlet on the lid, and run the pipe off the side, and have the pit vent continue up off the tee?

Of course, I plan to vent each fixture independently, as well; I have that part figured out.