What should I measure to identify the cables?
just find all the 12v ones and combine them
how do I put the psu in safety?
huh?
Do I have to connect the frame with a cable to the ground or do I have to put it in a wooden box?
no, it will provide the sufficient ground it needs inherently by the inverter based on the + voltage it outputs.
if I connect the 2 cables with different amperage and their sum gives me about 22A after I have to put a bigger type 1.5 or 2.5 mm cable?
sum them as close as you can you the PSU, and use a bigger cable from there to connect your stuff
the fuse higher than 22A?
the total output will be 22a based on the diagram on the PSU