A couple more questions!

We bought weld mesh, I know it's more expensive but far more reliable in keeping baddies out and will definitely last longer, so if u can manage in the long run it is better value for money. The only thing I would say about the coop is that if it is permanent you will need to clean underneath it and with only 18 inches you will be getting on your hands and knees. That's not really a problem just thinking of your back. Is the fence for the run or your garden?  If it's for the run are you going to cover it with mesh or something. Our mesh has been put within a frame so it can be lifted so I can dig the area over more easily. Obviously if you have a really large run that's not possible.
Hope it goes well

Not really sure about the fence height, someone else with a run on an allotment will probably advise. Flag stones are ok but it might be nice to have some of the area without just so they can scratch in it and even make their own dust bath, under the coop the stones would help with cleaning. Can't see why the 18 inches won't work, they might like to go under it for shelter. Ours is boarded on 3 sides so they can get some wind protection when necessary (just the area under the coop)

Most of the height questions can be answered with a single requirement:  Everything needs to be high enough so you can clean inside it easily.

I have a walk-in coop which makes regular cleaning a breeze.  I can go right inside with a leaf rake and fluff/turn the litter in a matter of seconds, so I do it every day.  If access was harder I might be tempted to take short-cuts when I'm in a hurry (or when I'm wearing my good clothes).

So if a 5 1/2' high run is high enough for you to clean it out, then it's high enough.  Personally it wouldn't work for me, so I would either make the run roof higher or do what gracie suggested and have removable roof panels.

Some of our hybrids and the Barred lymouth Rocks can clear a 6ft high fence, but others don't seem to bother.  A couple of our lower runs, I've covered with pond neeting from Willkinsons.  The birds try to fly up and hit the net, then they don't bother.

Predators like foxes could easily get in, but in our 9 years here, we've never seen a fox!