How many times can you copy a file from one HD to another HD without having the files coruppted or degenerated?
Infinitely. You're thinking about it like it is analog, but it isn't.
If your computer cannot properly copy files from one place to another without errors, it wouldn't be long before it wouldn't be able to boot anymore, and you'd have other VERY SERIOUS issues in everyday use. Windows creates, moves, and copies files around as part of just running everyday. Temp files are created, moved, copied and destroyed. Files are copied to and from RAM and to and from the swap files on the disk, and so on and so forth just as part of the normal operation of your computer. Modern hard drives have
substantial error correction circuitry built into the drives themselves. Without this capability, they wouldn't be able to function at all.
While a media file may be able to still play if errors are introduced (though there would be issues with playback in most cases), an executable file would not be so lucky. Data file copies on computers should be bit perfect every single time. If they are not, you have
broken hardware that needs to be replaced.
I dont know a ton about this, but yes simple copy and pasting does not "verify" that things were done without errors.
This is not entirely true. The simple Windows file copy process DOES have error checking capabilities built in, though it is not extremely rigorous. It generally relies on your hard drive to be doing its job properly, or to report read/write errors to the OS (which they do). That is a good tradeoff generally, because the specialized error correction circuitry in the hard drive is FAR faster than anything you could accomplish in software, and the drive has access to telemetry and other information on the state of the surface of the disk itself, which helps it to do it's job. If you try to do the same thing in software, your computer would run SUBSTANTIALLY slower in everyday use, for absolutely no benefit. Usually fingerprint verification systems (like MD5 and SHA) are used to verify a copy operation has succeeded when the transfer has happened via an unreliable or unverifiable mechanism, usually network transfers. So, when you download a big ISO file from the web, it might be a good idea to verify the SHA hash if you can, because transfers from the Internet can be unreliable (you can have a flaky router causing errors at any point along the transfer chain). Unless you have broken hardware, this should not be needed when transferring from one drive to another.
If you are really worried about it, and doing mass copies from one place to another, it is best to use an application that either does the copy operation in another manner. Sector level clone utilities are much more resilient, and much faster, if you are copying the entire contents of one partition onto another (so something like Acronis True Image or Clonezilla). If you are instead copying only a set of files, you can use a variety of copy and backup tools that create and verify file fingerprints to confirm the files were copied correctly (I really like SyncBack SE, which has this feature). This method will be slower than standard windows copies, but will verify that the copy happened correctly. I do this when I'm archiving things off onto disks that are going to be put away on a shelf, just to be absolutely sure that the mass copy happened correctly before I delete the original files.
However, this is absolutely NOT necessary unless your hardware or software is broken. If you detect EVEN ONE file copy error, you should immediately consider your system suspect. This, generally, is exceedingly rare. The only times when I've seen this with undamanged hardware was with external drives with very long non-active USB cables. However, in those cases, it was obvious something was wrong because the drive format itself was damaged and would not open in Explorer after the copy process finished.
Do you ever/or is there need to defrag the HD you store your music files on?
Yes, if you write to the disk a lot, the files can get fragmented, particularly if you run close to the total storage capacity of your disk a lot. NTFS is WAY better in this regard than the old Windows 95/98/ME FAT formatting system, so normally it isn't a huge problem. However, running a defrag on your system disk and media disk every so often can marginally improve performance.
In particular, my DVR drives in my system often get pretty heavily fragmented, which can impact performance and cause dropped frames when playing back HD video. It is simple to set Windows 7 up to defrag the disks automatically on a schedule.
Just set that up and be done with it.
In Windows 7 there is an option to optimize the (external) disc depending on what you store, why should this matter as everything is in digital format.
Well... Sort of, but it depends what you mean by "disc". If you are talking about external hard drives, you really don't need to worry about this, and the defaults should essentially always be correct. If you are talking about slow optical media (CDs, DVDs, etc) then that's another whole story.
On conventional media (hard drives), you can sort-of optimize the disk format depending on the types of files you store on the disk, by defining the cluster size used by the format. However, this has very, very, very limited performance impacts except for in extreme circumstances, and can cause problems if you store a variety of sizes of files on the disk. This should generally be reserved for experts who know what they're doing. The defaults are fine. Usually, the only time a regular end-user would see any benefit from a non-standard cluster size is if you ONLY store very large multi-GB files on a particular partition, and those files "grow" a lot over time (like a DVR drive). In enterprise applications with certain data sets this type of optimization is common (usually for big iron database servers).
For optical media, the CD burning application should take care of this for you in most cases. There are ways to manually optimize the burn to improve performance, but this won't impact playback quality, only read speed. These techniques are most common in large game installation discs where they need to quickly transfer massive quantities of (often very small) files from the DVD to your hard drive at installation time. Again, you don't need to worry about this.