How do I calculate the power dissipation of the transistor?
From the datasheet I found that Pmax=500mW.

The power dissipated by a resistor is the voltage across it multiplied by the current in it.
A transistor is exactly the same.
The power dissipated by a transistor is also the voltage across it multiplied by the current in it.
8V x 6mA= 48mW so the transistor will be slightly warm.
The signal is a sinewave that swings equally positive and negative so it does not change the power dissipation.

 

I have to replace all parts with nominal values, and then compare this to the originally designed circuit. Where can I find a list or something with the nearest nominal resistor/capacitor values?

 

I have to replace all parts with nominal values, and then compare this to the originally designed circuit. Where can I find a list or something with the nearest nominal resistor/capacitor values?

You could look at the website of your favourite electronic parts store or enter "Common Resistor Values" into Google like I did a minute ago.

Here is the list of common resistor values that I found. They are available inexpensively in 5% tolerance: