Can an electron gain energy by another electron? 
Is it possible for an electron to gain energy from another electron which is jumping from higher energy level to lower energy level, and shifts to higher energy level?
 A: As John said in the comment, yes!
It is called the Auger electron. One electron from inner shell is ionized by an external field, like a laser, which we call this electron as photoelectron. Then an electron in the higher level should occupy the vacancy from the missing electron. So it lands from the higher level to the vacancy. This causes a photon emission. This photon in turn hits another electron in a shell and pushes is out of the ion. This electron is called the Auger electron.
Another way is an electron that is ionized by laser field, gets accelerated in the laser field, and then returns towards its parent ion and collides it. Usually this produces an XUV photon but there is possibility to shoot another electron out of the ion. Search for "Non-sequential double ionization" to learn more about this.
A: https://en.wikipedia.org/wiki/Townsend_discharge is another example in which free electrons collide with and give energy to other electrons. 
A: Yes ofcourse. 
1- by collision then they behave like a particle.
2-when one electron emit photon.. The photon collide with other electron.then photon get absorbed
