The freeware version of Killdisk is limited to a one-pass overwrite with zeros. Darik's Boot and Nuke can do a DoD 5220-22.M overwrite (among others) which is more secure (the pay version of Killdisk can also do this).
Neither of these utilities works in Windows. They both boot from a DOS floppy, CD-ROM, or USB flash drive.
Nope, full format doesn't overwrite anything except the partition table, MBR, partition boot sector, and a few sectors of file system entries. All other data is still fully recoverable after a full format.
You must use one of the overwrite tools (there are others than the ones I mentioned above) to actually erase data.
You need to use a wipe utility. Some are available as shareware or freeware on the Web. AFIK, Norton Utilities includes a wipe disc utility. You will need to run it at government security spec level to ensure that the drive is wiped completely. Note that it is necessary to run the utility 3 times to ensure complete overwrite of your existing data files with a random pattern of 1 and 0. There are 3 layers of writable media on a hard drive, and old data can be recovered from the lower layers even if there is "new" data on the surface layer.
Formatting the disk will NOT delete the data. Deleting the files, evenm if you turn off the Recycle bin will not remove the files.