is it that alright if I put e.g. 2W 4Ohms speakers on it?
Straight up answer to your question is no.
Well because an amplifier outputs power at a certain rate determined by gain.
Speakers have a thing called Impedance measured in Ohms... so your speakers' impedance in this case is 4 Ohms.
What would happen if I do so? what is affecting it?
Improper impedance matching can lead to excessive power use, distortion, and noise problems.Think of it like this if you Decrease your resistive impedance You will allow more electrons to pass through the speaker... therefore allowing the amplifier to pump more unnecessary power to the speaker... which will end up bad like a blown fuse or a burnt amplifier.
It is an easy fix however. Capacitors are the total opposite of Inductors. Coils are the same thing as Inductors, you will find coils inside of speakers...
The most probable solution to your problem is LM386 op-amp to match impedance and drive your 2W speaker all the way or put a 4 Ohm resistor is series with your speaker. Does it automatically reduce to default volume even I put higher Wattage speakers?
Higher wattage speaker just means it can handle up to that amount of power, yes the volume will sound a bit quieter on a higher wattage speaker. An LM386 op amp will drive a 2W speaker easily.