@jens m.#48100 at the end of the session the Zero Position is wrong (1 hour rotated)
This is indicative of the Daylight Saving Time bug in ASIAIR (or I should say, incorrect implementation of Daylight Saving Time support).
You might try this experiment, which does not need a dark or clear sky. In fact, daytime is better since you can actually watch the mount's movement.
Try to level your tripod (at least the East-West direction) to better than one degree before placing the mount on it.
Connect ASIAIR to your mount, as you normally do.
Now, with a planetarium program (like SkySafari or Stellarium) see if you can find a star that is about 15 minutes in RA and East from the Prime Meridian. You can also choose direct coordinates in ASIAIR's GOTO panel if you cannot find an appropriate star.
Issue a GOTO to that star.
Now find a star (or coordinate) about 15 minutes West of the Meridian, with as close a declination as possible to the previous star.
And issue another GOTO while watching your mount. Does the mount move the OTA directly from the East star to the West Star? Or does the OTA take a route that slews it past the pole, presumably the North Celestrial Pole since you are aus Deutschland?
If it takes the long route through the pole (a Meridian flip), then the local sidereal time of the ASIAIR and the mount are in sync (so there should be no problem with UTC, UTC offset and longitude discrepancies).
However, if the second GOTO takes a direct path, you are bitten by the Daylight Saving Time bug.
The way to avoid the ASIAIR bug is to tell your mount (it should be a parameter in the hand controller) not to use DST. I.e., turn off DST, so that the mount thinks it is operating in Winter Time ("standard time"). On top of that, if your mount has GPS, see if you can disable it, and let the ASIAIR push date and time from the iPad to the mount. These two things alone might make your mount return to the correct Zero position (and also perform meridian flips at the correct time).
The fact that ASIAIR does not understand DST is probably what caused your 1 hour error in the Zero position. Since ASIAIR is dumbed down to not understand DST, you also need to dumb down the mount to also ignore DST.
If ZWO has used UTC as the absolute standard instead of mucking with local time, then DST would not even be an issue. It is not like the 18th Century sailor who does not know the precise time at Greenwich to determine his own longitude. iOS has system calls to obtain the UTC directly without going through local time, and it also knows the longitude of the tablet (thus knows the time offset from UTC), so there is no explanation why ZWO still struggles with DST.
You can also force a Sync To Mount from the ASIAIR Telescope Setup window. (The "sync to mount" is usually executed when you connect the mount to ASIAIR, but tapping on Sync To Mount will make sure it happens; also in case GPS or something else screws up the time.) This will force the mount to take the latitude, longitude and time from the iPad.
Again, before you Sync To Mount, make sure DST in the mount (usually in the hand controller) is already turned off.
All of these things should help sync the ASIAIR and the Mount so that they both have the same Local Sidereal Time.
After this, test the east and west stars again.
The other recommendation I can give is to use as little automation from ASIAIR as possible. Very often the worst bugs are in their attempt to make things easy for the beginners. So, turn off Auto-centering (unless you trust it to do a correct Meridian Flip while you are asleep).
After a plate solve, manually issue a Sync And GoTo from the plate solve result window. Don't let ASIAIR do the Auto Center until Sync And GoTo works properly.
Sync And GoTo is actually a two-step process. What the Sync command does is to send the plate solved coordinates over to your mount to tell the mount where the OTA is really pointed to (and not where the mount thinks the motors are pointed to). Then, the following GoTo will issue a GoTo command to the mount to tell it to move to the original Target. If the Sync position is different from the Target position, the mount will execute the correct movement -- as usual, ASIAIR does not do any difficult maneuver except to command the mount to do the actual hard stuff.
The Sync and GoTo process is completely independent of the direction of the DEC+ or DEC- buttons. It depends only on GoTo and the Sync commands on the mount to work properly, and it should be pretty error free, whether ASIAIR understands your mount or not. ASIAIR simply depends on your mount to understand its own coordinate system.
Chen