K8084 + tr8040

No, supply voltage of K8084 is 2x12V, while TR8040 delivers 2x25V

Rectified 25VAC will be close to 36VDC.
Not sure 7812 can handle this. Maybe there are other 12V regulators that can handle up to 40VDC at the input.
Negative version of 7812 is 7912 (beware: different pin out)