Well, from what I know right now, TrueCrypt 7.1a is the latest known secure version of TrueCrypt, since the project was discontinued. The first report of the security audit declared that version safe to use, but we'll only really know once we get the second report. For more information, you can take a look at the audit's website here:
May I ask you which version and edition of Windows you have? If you have Windows 7 Ultimate/Entreprise, or Windows 8/8.1 Professional or Entreprise, you have access to Windows in-built BitLocker to encrypt your HDD and it's content. See the article here:
Otherwise, there's other alternatives to TrueCrypt and BitLocker, such as DiskCryptor and VeraCrypt. However, you should take a look at their requirement to make sure that they support your version of Windows.
As for your last question, it really depends. Is the back-up "online" or "offline"? It also depends if you bring it with you often or not. If there's a chance that this back-up drive might get stolen, I would encrypt it as well, just in case.