Floating desk on concrete block wall
The hardest piece of your question is the sag and being able to support the weight of someone resting at the mid point.

A 2x4 ledger attached to the 3 walls to support the desk solves everything except the sag.  

At ~7ft across, for the sag the best option is probably metal angle iron set back 6" from the front and secured to the side walls using either a bracket or the ledge used to the support the desk.  Maybe a 2"x2" angle iron at 3/8 thickness.  You could also use a couple brackets from #2 to add support to the angle iron from the back wall.