>> Upon testing, I realized that the data from the mount seems not to be transferred to ASIAIR,
>> it just keeps displaying zero values. Do you have an idea, what I am doing wrong?
No idea. Do a sanity check to make sure that the menu in the hand controller selects the RainbowAstro protocol instead of the LX-200 protocol, and make sure too that you are selecting USB instead of WiFi. And for good measure, sync the mount to its GPS (press and hold ENT on hand controller once GPS location and time is received).
If longitude field is undefined, I can understand why your mount does not move.
On three different iO devices (two iPad Pros and an iPod touch) and a Samsung Galaxy Tab A, once connected to "RainbowAstro RST/MC700GE-II" (Serial/115200 baud), everything in the Mount Info section gets populated properly. Except for the Time Zone -- ZWO told me that they could not pull Time Zone data from their RST-150h (same protocol with our RST-135), so Time Zone always read UTC+0.
With the mount in the home position, the DEC field in ASIAIR Telescope Settings should read 0, with the RA reading local sidereal time minus 6 hours. The RA will also increase with time, thus tracking the west horizon. With iOS, the Time field in Mount Info is only updated when you select the Telescope Settings window, but it is updated every one to 5 seconds on Android -- there are numerous irritating bugs like this in ASIAIR.
You should also see the tracking (green) LED on the mount flash when you turn the Tracking switch in the Telescope Settings window on (and stop flashing when you turn the tracking switch off).
The "Start" button of "Goto Home Position" should also start the mount hunting for the home position.
Finally, in the main ASIAIR window, you should be able to pull up the small "goto" sub window. And the direction buttons there should slew the mount.
If you have not be following my earlier posts on the RST-135, please be aware that when you change the Speed slider in the Goto sub-window, it will change "Speed 2" in the hand controller to match the speed of the slider. I.e., the ASIAIR hijacks "speed 2" in the mount to use for slewing (you can see the red Speed 2 LED on the hand controller flashing). As a result, when you leave ASIAIR, you will need to go to the hand controller to set Speed 2 back to your default before using the mount without ASIAIR.
With the ASIAIR, you can use the RST-135 most of the time without the hand controller connected. You do have to make sure that the clock in the RST-135 is synced to GPS (which is in the hand controller), though. I have found that I can run a couple of days without re-syncing the RST-135 clock to GPS. In earlier versions of ASIAIR, we could push time from the tablet over to the mount by using the Sync To Mount button in the ASIAIR Telescope Settings window. Unfortunately, that is no longer available in ASIAIR v1.3, so you need to use the hand controller's clock to GPS every so often.
Regards,
Chen