What is Redox reaction? Is it really possible?
I think you mean Redox, which is a portmanteu of Reduction-Oxidation. An easy example of redox is the Haber process (nitrogen and hydrogen form ammonia)

$$\ce{N2 + 3 H2 &lt;=&gt; 2 NH3}.$$

In the Haber process the nitrogen is reduced (the oxidation state changes from $0$ to $-3$), and the hydrogen is oxidized (the oxidation state changes from $0$ to $+1$). In that redox reaction, both oxidation and reduction take place, as you said.

There's no oxidation without reduction and vice-versa. The electrons lost in oxidation have to go somewhere! If they wouldn't, then there's no reason for the reaction to occur in the first place.