In the mean time, I have tried the coil, and it works. I have sparks from +/- 5 inch (15 cm), but without tuning. First of all, I have to made all things safe, and I have glued some things to enforce the complete Tesla. Then I must place an isolating tube over the secondary, on the underside, to avoid sparks to the primary. The Tesla transformer is for demonstration on different places, so it must be possible to disassemble it.
The frequency is +/- 350 kHz.
PS: paraffin is a cheap method to isolate or protect or repair things like coils, capacitors, tht's aso...