kitce:
The questions are:
- Can I read the sound level directly from the audio jack with Arduino?
- How should I connect the electrical components?
- Do I need any resistor or capacitor? Why?
No, not directly, you need two resistors for coupling the audio signal into Arduinos analog input, i.e. A0.
I've searched acircuit schematics for you
This circuit can be used for coupling the audio output from your smarthone or "line out" from your PC into Ar duino:

You can leave out resistor R1 and capacitor C, but you need those two 100K resistors R2 as voltage divider.
Value of R2=100K is not critical.
You can use R2=68K or R2=82K as well.
But don't use this circuit with coupling of output from power amplifiers, which could provide dozens of volt output power.
This is circuit is suitable for PC "line out" audio level or for audio output from your smartphone only, not for output from power amplifiers.