do you know somewhere where i can get one for about 20 euros?
Sorry no.
Do you think I will have enough precision for what is required?
Yes the saw cuts needed are not very precise, you just need to cut the length to a few mm.
Where to get the belts from?
http://www.mendelfactory.com/index.php?cPath=28
And how to make sure the motors I'll buy will fit with the printer?
Look at the size of the hole in the printed part or the shaft size of the recommended motor and make sure your motor is the same size or bigger, then you need to drill it out.
i don't have any machines as we're doing maths, physics and chemistry but no engineer work.
Every place that has done physics that I have bee to has a small workshop somewhere. Ask around the teachers maybe they know somewhere that you don't know.