Mac keeps asking for password to put apps in trash?

Ever since I made a new account on my mac (which mind you, doesn't even have a password) Certain apps will go in the trash, and other apps will not go in the trash directly..you have to go into finder, trash, then it asks for your password. I don't ever remember having to do this before I made the new account, and it's very frustrating😠

I have tried repairing permissions time and time again but to no avail. This annoys me so much I wish I could just reinstall the whole OS, but i don't have the disc. I'm using a late 2008 Macbook with snow leopard..any suggestions?

The exact window that comes up says "Type your password to allow finder to make changes." in the details, it says "Right: com.apple.desktopservices" "Application: Finder". I haven't found anything on the internet that matches the same issue have, so please help me. Thank you!