Do not understand why current flows in undamped oscillator circuit, and getting troubles in practice
What am I doing wrong?


You picked a circuit that does not show any biasing arrangement for the transistor nor shows polarity information on the transformer windings. Likely is that you found the circuit on some website that is trying to explain the functionality of an oscillator and, to make it easier on the learner, they omitted bias arrangements and transformer winding polarity in an attempt to make things clearer (never really a good idea).

Given that I see numbers pointing to various points on the circuit it looks like me that the diagram originates from a patent document and these are notoriously light on information that isn't relevant to the patent.