Hi devinwe,
Windows always immediately deletes items from any removable media. The Mac OS does not. They do have a common method of creating an invisible Trash folder on each fixed volume attached. Meaning all internal and external hard drives.
Where Macs and Windows differ is that the Mac OS creates these Trash folders on
all storage devices, making it possible for you to always pull something back out of the trash. So when you put something in the trash of your Jump Drive on the Mac, you then have to empty the trash to remove it, just as you would with any hard drive.
Any file or folder that begins with a period is invisible on the Mac. This is common to pretty much any Unix OS, over which OS X is built. Windows doesn't care about this rule, so you see any files in Windows that you wouldn't when viewing the drive on the Mac. You can delete them if you want, the Mac will simply recreate them every time you use it there.
A .DS_Store file is what OS X uses to remember the size, viewing option and position of a folder window. It hurts nothing to delete them, except that the window it belongs to will revert to a default display the next time it's opened.