The answer to both your questions is quite simple.

1. Code prohibits running a horizontal vent line under the floor.

2. Code prohibits notching the underside of a joist and it is extremely restrictive in how or where we may drill holes through the joists.

Thanks. They're not going to notch the new joists, there will only be holes drilled through the center of the joist. I'm going to call the building inspector on Monday and get a permit so I can hold people to their work.

I wonder how they'll get the tub venting done, maybe run it up through the attic and tie it in up there?

If you are close enough to the main stack you may not even need a separate vent.