Once you have uninstalled a program it is no more, although some traces can sometimes still be found if the uninstaller wasn't propperly made, or you've made shortcuts to the program in places that the uninstaller didn't expect. In that case you'd delete any such shortcuts and the Folder in Program Files which originally belonged to that program (and delete them from the recycle bin).
As for the second question you raised, that information is relevant to sensitive files which must be completely removed. Once a file is deleted a computer the computer marks it as not there, and that hard disk space as free to use. However to save time and wear on the hard drive it doesn't actually overwrite the space until something else is written there. If the file you've deleted contains your personal bank details, it may be worth your while "shredding" the file by covering it with random data. If for whatever reason you consider the existance of this program to be sensitive material you could try downloading and running one of the many free space shredder programs, alternatively you can consider the program gone once its uninstalled.