4seventy, thanks for your excessive and unjustified confidence in my limited knowledge!
Hubert, I will try to answer your questions anyhow:
I have just acquired a complete set of these Vienna mounts on a Kahles Mignon 4x.That includes the front and rear lower bases.
Rear lower base? Please post or send photos of your mounts. pm sent. What gun do you want to mount it on?

A-Is there any tension between the front and rear bases when installing the scope on the rifle ?
No tension, just a snug fit between front base and rear anchor screw (on a Mannlicher-Schoenauer)

B-That is , does the scope require a firm push to click on to the front base?
No, just the resistance of the spring-loaded locking levers = Schnäpper has to be overcome.

C_Or does the scope click on without tension ? That is , clicks on freely .
See B

D- Uninstalled the front base has a small amount of front and back movement .It seems to me that a tension is required to take up this movement after mounting on a rifle .
No tension, just a snug handfitting front-rear.

E-Thus is the front lower base worn ?Or is this movement normal in uninstalled mount ?
Most likely not worn. As in most Wiener Schnäppermontagen the only windage adjustment is by driving the front base sideways, using hammer and brass punch, there must be some play here.

I have not yet mounted my Kahles Mignon 4x shown in this thread above, but I intend to do so on my M1900 Mannlicher-Schoenauer.

This is the way I figured out so far: First I will soft solder the front base to the barrel reinforce. Next I will use my Tasco boresighter to determine the exact position of the "rear base". On Mannlicher-Schoenauers this "rear base" is merely a large-headed screw in the left top of the receiver bridge (ok, I know this bridge is split). The dog-legged rear top of the Schnäpper mount goes under this screwhead with it's pronged lower end. I will place this screw just slightly forward of the indicated position and lock it so that the prongs just slide under it's head. Doing so will allow me to file out the cutout between the prongs of the rear top so that the scope is held snug, but without tension, between front and rear bases. On these Vienna style mounts the recoil stress is taken by the front mount only.