Ok. I done some tests and it's still very confusing.
I have pointed/tested it at 2 locations on opposite sides of the house, where I know the local masts are, and tried to aim in a similar direction like the rest of the houses around. Results are as follows:
1. 4G Router - Antenna. Speed was similar to the one without external antenna, no real change here
2. 4G router - booster - antenna
2A. I clamped the antenna to the window wing, and could test position a bit easier. Temporary solution but good for testing. On some locations 3 green lights (for the signal bands I assume) on the booster were on, but the router showed "No Service" message. Also no internet.
2B. I just propped it on the window sill: signal lights for 3 bands on the booster were off, not even blinking, but on the router I had max bars for signal / service ...but No internet! On router settings I changed it from 4G only to auto and it started to show a very slow internet access...
I was thinking it was maybe only getting the 3G signal through, but the router did show 4G... which was weird.
I am really unsure what to do next... maybe my kit is wrong? I was hoping to save some money and not call the company to install their own equipment as they would charge arm and leg for it ...but I dont know enough about the subject to do it myself I think...