So I get the gentle acceleration.
I understand not over-revving.
I don’t get “coasting” which I had always been led to believe you shouldn’t do as it means you’re not in full control of the vehicle, but I’ve been advised to do it. 
Any thoughts?
It’s the eco roll mode on Mercs and Volvos mainly. On a downhill it will drop into neutral and coast down until your speed drops back down where the box will re-engage. If you set it up right on the dash you can set an upper speed too where exhaust braking will prevent you from exceeding a certain speed. Good for motorways, but turn it off in urban areas as it drops into neutral as you approach roundabouts, junctions etc and gets on your ■■■■.
On the Volvos you want the exhaust brake stalk in the 2nd position from the top and it will show E+ on the display. To set the overspeed limit, wait til it starts coasting down a hill then use the rocker switch on the end of the stalk to adjust the overrun speed from 4 to 15kmh. Can’t remember the Merc set up as I rarely drive them now.
There are many aspects to Eco driving. The point is to complete a given distance using less fuel. Here are some thoughts
Lower the engine speed by changing into a higher gear earlier
Lift off accelerator earlier. This uses the vehicle momentum and basically provides a distance where zero fuel is being used.
Use cruise control where appropriate to minimise engine speed for distance travelled
Lower road speed more before changing down gears then block change into a gear that will not cause engine speed to increase much.
Use retarder brake to slow vehicle down by lowering engine speed.
There are many other techniques as well as these few. These are just a few driving tips for Eco driving. I havnt even started on aerodynamics, weather and route planning, necessary weight carried etc etc