Just a small point - when you said " Because I'm only giving one input to the first transistor Q1, the second Q2 does not do anything, so I could directly put its base to 0V and turn it off? " you don't turn a transistor off in a differential stage, you keep both conducting the same current.
As others have said, you only need base bias resistors to go between the bases and ground (0V) - but you do need to make the bias resistors the same, or the voltage drop on each side will be different. So don't connect directly to 0V but use a resistor.
The capacitor to ground will hold the base grounded to A.C. signals. That's why there is a capacitor there.

 

I understand. Basically, since both transistors are symmetric, the current Iee will set the bias Q points of both transistors. And If I want to have a common mode, all I need to do, is use the same base resistance to ground for both transistors. If I want to create a steering current, probably I have to use different values for each RB, depending how much current I want from each collector.

 

I understand. Basically, since both transistors are symmetric, the current Iee will set the bias Q points of both transistors. And If I want to have a common mode, all I need to do, is use the same base resistance to ground for both transistors. If I want to create a steering current, probably I have to use different values for each RB, depending how much current I want from each collector.

If you set it so that the collector currents are equal with no input signal, you will have lower distortion. A common cause of distortion in power amplifiers is that the input differential amplifier is out of balance.