Quotation: It is good point to think why my 2nd circuit is wrong. But can you define qualitatively? If I use my 2nd circuit will my load get destroyed?
Mustafa, your circuit is not "wrong". For my opinion, a circuit never can be "wrong".
It only can work as desired - or not. To answer your question: No, it will not be destroyed.
However, your second circuit is not an amplifier that is able to amplify voltage differences (which is the task of a differential amplifier.)
As I have told you in my first reply, the current fluctuations through the common Rc cancel each other. As a result, there will be no output voltage resulting from an input difference.
To understand this you should try to become familiar with the principle of the classical diff. amplifier configuration.