Something is wrong with that. The frequency should depend on the
capacitance at that node (top of BB105 to ground). If it doesn't, then the
oscillator transistor (the one on the left) isn't oscillating; the
amplifying transistor (the one on the right) is. I think the oscillation
in the left transistor happens because of feedback internal to the
transistor, because no added feedback is shown on the schematic. This
means that exactly what happens in simulation, is strongly dependent on the
device models used for the transistors.
Do you think I used the wrong models or the setup of my circuit is wrong?
Are the two halves also coupled, with a K ?
No they are not. I thought if it is a coil with tap I can separate it without using this. On the first hand I don't know how to use it. And on the second I thougt, if it's ideal conducting the K doesn't matter.