12V battery charger does not work
there is no capacitor for smoothing the waves

That's fine for charging a lead-acid battery. The control circuitry runs off the battery between peaks of the mains waveform. Charging a completely flat battery would be interesting, though you shouldn't let a car battery get completely flat.

And by disconnecting gr1 from (-) plate of 47u the following wave will be gained (smooth voltage waves plot): However in either case the amplitude is too low.

With that connection omitted the transformer output seems to be ~30 Vpp on both legs of the transformer. Allowing 1 V drop across the thyristor means there's 14 V to charge the battery, which seems reasonable. So you seem to have a problem with your control circuitry rather than your transformer.

the anodes go to GND!

Unusual but fine. The thyristor gates need to be biased positive with respect to their cathodes to turn them on. The configuration used saves the need to have a secondary control circuit power supply at somewhat more than +14 V to turn on thyristors in the positive battery supply line.