2-) What's the output voltage of a standart mp3 player? Can it be 300mVp as I read somewhere?
Yes, 300mV peak is reasonable. MP3 players can give higher output than that with loud recordings, but there is a volume control to turn it down.
3-) When I assume ß = 150 and input = 300mVp , the output is -2,13Vp . I guess it gives 1w power to speaker. Is there something wrong?
Yes.
Signal current into base = 300mV pk / 90K = 3.33uA pk
Signal current out of collector = 3.33uApk * 150 = 0.5mA pk
With no load connected:
Output voltage = 0.5mA pk * 8K = 4V pk
With 12K load added:
Output voltage = 0.5mA pk * 8k||12K = 2.4V pk
With the 4 Ohm speaker:
Output voltage = 0.5mA pk * 4 Ohms = 2mV pk
1-) Is 2n2222 ok for this circuit?
Not if you want 1 watt peak power to the speaker. 1 watt peak into 4 Ohms = 2V peak * 0.5A peak, so the amplifier needs to give +-0.5A current to the speaker.
To do that, the DC current through the transistor has to be more than 0.5A because it also has to give signal current to the collector resistor.
If a 10 Ohm collector resistor is used, that will need +-0.2A of signal current, so total signal current from the transistor = +-0.7A, so a DC current of 0.75A through the transistor will be just enough.
If the DC voltage across the transistor is 4V, then the power dissipated by the transistor is 0.75A * 4V = 3 Watts.
You need a transistor that can dissipate 3W of power and conduct 0.75 amps average current, and 1.5A peak current. That is too much for a 2N2222. A medium power transistor such as a BD139 should be OK if it is on a heatsink.
The next problem is that the current gain of the BD139 will be very low (maybe 20), so you need another transistor between the MP3 player and the BD139.