Can I create a flower/grass bed in the middle of concrete driveway

Only issues I can see are if you dive over the plants! - other than that it is just based on how well you install the mesh, etc.

Yes that is possible and unless there are pipes running under your drive there will be no issues as long as you dig down deep enough and fill with a good type of soil.

Within the civil engineering industry to place landscaped and architectural features within a concrete or hard scaped area would require tree pits. These would be sealed units within a concrete car park (example) They can be made out of pre fabricated reinforced concrete or quite simply they would be a hole dug and surrounded with a geotextile weed membrane and a DMP visqueen then filled with a topsoil material. Basically it would keep the two areas separate from each other. No roots damaging the structural integrity of the surrounding car park and no chemicals washing in from the concrete. These pits can be fitted with there own irrigation and drainage systems to provide a secure growth environment for plants/trees. In your case i would ensure that the planter is sealed from the drive way keeing it seperate. if you want to combine drainage i would place a terram 1000 membrane onto the bottom of the planter and peice the DPM on the base only. This would require watering during the summer months. hope that helps.