As I've commented, I find your first question a bit vague, so I'll go on with the rest:
Moreover using a software like this, would you keep a security not encrypted copy of your private data, for example on a dvd or a usb hard disk, in case of software failure or error, or you would only rely on the software?
How much is Truecrypt reliable ? Can it be cause of data losses, due to a malfunction, I mean not due to a forgotten password, but to an internal error of the software ?
Truecrypt is widely used, but you can never guarantee that it's completely free of bugs. For example, when it's in the middle of a write operation and the power fails, the disk won't complete the write, possibly leaving the file corrupt. Not Truecrypt's fault, but it can happen.
So yes, if the data is important to me, I would always keep a backup. You can keep an unencrypted backup, but what's wrong with storing an older version of the encrypted file? (Truecrypt stores the encrypted virtual drive as a single file.) Mount the file, read/modify it, and unmount it when you're done, just like you normally would. Then, test if you can decrypt the saved file (so that you know it's stored correctly), and copy the file. That makes sure you won't loose (much) data because of something caused by Truecrypt itself. The more regularly you copy the file, the less work you could loose of course. Just like with normal backups.
Then there are issues like drive crashes, the chance on fire... So an off-site redundant backup would best protect your data (all the wile keeping it encrypted). Just like with normal backups.