The debug dump files are error reports and information relating to the content of your RAM memory when you have a Blue Screen or other system error.
They are what you will send to Microsoft if you choose to do that after any pc crash.
You don't need to keep them and can safely delete them as and when you like.
As for "old" files...these are files and folders on your syatem that have not been accessed for a period of time......compressing them is a way of reducing the space on the hard drive they take up.You can still access them if you need to but they will need to be decompressed before thay can be read, which will slow the computer down a little bit.Not worth doing unless you are getting short of space on your hard drive.
DO NOT DELETE THESE "OLD" FILES......
They are all most likely needed or essential files.Such as the vast majority of ,say your MP3 collection which has not benn played for a few weeks,or important saved documents or mail.