No such tool exists. You are talking about at least three different classes of programs.
Scanning the HDD is something best done when booting from a minimalist OS on a CD or something. Defragmenting is a tool that should have died about 15 years ago when it stopped being useful, and file backup is yet a third completely different type of program.
There might be some "suite" programs that will have all of these things in it, but I tend to steer clear of those. While it is certainly convenient to have only a single place to go to update all of these programs, it's similarly convenient for any ne'er do wells interested in attacking your system. Those suites always use a lot of shared code, so if there's ever an exploit found in that shared code, it'll affect pretty much the entire suite.
But let's also just skip to what is likely a follow up question. There are no diagnostic programs for software. The closest you can get is debugging tools, but those are only useful to programmers. There are just too many possibilities for what can go wrong with software to be able to make a diagnostic tool. The best diagnostic tool you have for software really is Google. Any time you come across some error, you enter it into Google and see what results pop up.