Exactly what would happen with a sealed system. I agree that it is better to have the cold water storage cistern at a higher pressure (height) than the F & E, but I asked this question on this forum and consensus was that there is no regulation on this (and, in this case, it would not really be practical to raise the existing cold water storage cistern to a higher level just in case, one day, the coil fails). I would have done the same as the installer has done.
Cistern must be fully supported on close boarding. Which the F & E seems to be. Looks like chipboard or OSB where I would prefer to see 18mm hardwood ply, but perhaps it's a matter of preference. The boarding is on three supports, so it won't be going anywhere, after all.
I am, though, suspicious that the combined cold feed and vent pipe coming out of it may not slope down away from the cistern as it should do. I would also expect the cistern to be lidded and well lagged when the work is completed.