I want to know if a PCB board is only having differential pairs to route and they are routed on top and bottom side of the board, then is it good practice to put two GROUND plane back to back (signal-ground-ground-signal) in PCB stack? If it is not then please suggest the right way to route the board and right stacking of PCB.
I don't see any problem with doing that, just tie the two ground layers together with vias. Now how many vias I couldn't answer but I'm sure a magnetic 3D solver can tell you if you need more or a different distribution. Though intuitively I doubt there will be much of a difference between 10 vias or 100 vias. I suspect the vias tying the connectors to both ground planes will be enough.
Probably means don't try and have a 3 layer board made or have a layer stack up that is not uniform. I would suggest making the stack up using standard layer thicknesses (which I can't quote as I haven't been designing boards for decades).
Yes, keep the stackup so that it is balanced about the Z axis, nothing to do with your diff pairs - more about NOT thinking - "oh hang on I only need 1 gnd copper layer" and making an unbalanced board.
Copper layers are always added in pairs, its a manufacturing thing, even copper layer PCBs will always cost leass than odd number PCBs, odd numbered copper layers are very rare....
I don't think odd layer number PCBs are industrially manufactured, the manufacturers that offer this will probably use their higher layer count line and etch one of the layers completely blank. So just make use of that extra layer for an additional ground plane instead.
If you look at multi layer lay ups both core and foil, they are all geared up for even number of copper layers, you can have odd copper layer boards made but they cost a ridiculous amount and are not worth it, I had to do one once for a pedantic engineer, who wanted his own way, it cost an arm and a leg... hi insisted even though he was given advice not to go that way, happily he soon left the firm by mutual agrement:wink: