Daisy, Unless I am wrong I believe the case is covered with fabric or a paper like wallpaper. Those are probably stains. I would recommend trying to use different cleaning products in a small area. Start with the mildest one and progressing up from there. On my computer it looks like it might be rust stains. The inside of the case us often just thin paper and cannot be cleaned on the ones I have had.
On the tears I generally use a simple waterproof glue and work it into the area.
Good luck to you.
~Grant~