The transformer parameters are core size and material, air gap, winding turns and wire gauge, required layer and inter-windings isolation. You should be able to determine it even from a defective transformer, as longs it isn't fully burned.
I understood now about the relation of the two schematics, you're of course right, that the auxilary 5VSB converter from post #5 is exactly indentical to your circuit. You have also the windings polarities correctly marked. I also agree, that the replacement of low voltage transistor C945 isn't critical, any small NPN transistor (e.g. 2N3904) will fit. Using a slow 3A diode (1N5408) for the RCD snubber isn't that good, i fear. A fast recovery 1A rectifier should be used in this place.
A problem of the circuit is, that if the transformer feedback doesn't work, the output transistor will be overloaded and burn very quickly