Grounding for surge protection for telephone/internet/data lines
Yes. Having a suppressor just between wires wouldn't suppress the common mode transient, present in "both" wires. I said both, because the ethernet has 8 wires, so it makes further complicated to have supressors placed in between each wire.
I don't think so. Where does your ISP cable comes from? 
Without connecting the ground wire, the protection won't work. There is no schematics or photo of the centrally positioned GDT, so these are only guessings.
"Commercial grounding plugs I found so far have 1 MOhm resitance" . It could be that you are wrong? 1M resistance is for some ESD mats, bracalets - this is not grounding. Grounding is a direct connection to PE.