This only answers one part of your question, but I think it might be the main place where you are misunderstanding.
How can the Ohm Law be applied in this case?
"Ohm's Law" isn't a law for all circuits. It's a description of one particular type of component: the ideal linear resistor.
It doesn't matter how your power supplies are arranged in your circuit. Ohm's law has nothing to do with power supplies.
The general laws you want to consider that describe how currents and voltages relate in any circuit are Kirchoff's Current Law and Kirchoff's Voltage Laws. These laws, along with specific current-voltage relationships for each type of device (one of which is Ohm's Law), are the main tools for analyzing circuits.
In your equivalent resistance equations, you are missing the fact that a voltage source has impedance of 0, and a current source has infinite impedance. Anything in parallel with 0 impedance still results in 0 impedance. Likewise, anything in series with infinite impedance still results in infinite impedance.
To help convince yourself, try putting some real number on your top example. Pick some values for the voltage, Rp, and R. Now put different loads on the result and compute what the voltage on the load is with and without Rp. You will see that Rp doesn't matter. The voltage across the voltage source is the specified voltage, by definition of what a voltage source is. Put another way, a ideal 10 V source always gives you 10 V, whether someone else is drawing 10 mA, 10 A, or nothing from the same voltage source.
Best Answer
The transform will be to a current source with infinite current and therefore (so the mathematicians say) the voltage will be finite across a zero ohm parallel resistor.
Consider a 1v source with 0.001 ohms series resistance - short circuit current is 1000 amps and therefore the equivalent current source is 1000 amps in parallel with 0.001 ohms.
Keep moving the goal posts upwards and you of course get very big currents and very small resistances but it is just a theory and at this sort of level has very little practical importance to many things.