Is transformer output a real voltage constant source (not current), as seen a circuit next to it apply current divider behavior having no the first resistor except usual rectifying diode in parallel to its RC snubber ?

 

I don't think so. A constant voltage source will supply any amount of current into a load. I don't think a transformer can do that.

ETA: The ability of a transformer to "look like" a constant voltage source depends on the relationship between the load impedance and the voltage source impedance on the primary side as the following simulation demonstrates.



For load impedances of 1Ω and larger the output does look like a constant voltage source. The traces for 1, 10 and 100 are all overlapped. Change the source impedance of V1 and there will be a different load impedance above which the secondary looks like a constant voltage source.

Since transformers are modeled as coupled inductors there will also be frequency effects.

 

In addition to the source supply impedance each transformer winding has inherent resistance and leakage inductance, considered as series elements in the circuit. Those also affect what voltage is seen at the output terminals as the load current changes (due to the resistance) and frequency changes (due to the inductance).

 

It depends on what is supplying the transformer. The output reflects what is going on at the input (with the addition of all the parasitic components)

 

For an ideal transformer, the output reflects the input source.
So the output will be constant current for a constant-current source, and a constant voltage for a constant-voltage source.