Re: framing a lower ceiling edge
I've seen these soffits done two ways, one is to lap the end of the horizontal and vertical member and nail together, the other way is to butt one into the other and use a plywood gusset on the side or both sides to connect the two firmly.
The vertical member would be nailed to the side of the above ceiling joists, the walls could be attached to a ledger or bare stud if the wall is open.
If you're attaching the vertical members to the surface of the ceiling, then I'd recommend lag bolting a ledger into the ceiling joists and face nail the vertical member to the ledger. I actually just used this method in a garage conversion that required a soffit to cover exposed mechanicals.
On another project that I was party to where we did this, we also ran the drywall horizontal drywall 4" past the vertical face and installed a piece of molding to create a bit of a pocket. Inside the pocket was placed rope lighting to give the recessed ceiling some back lighting. The lighting really set off the whole area.
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