It also includes encryption, but don't rely on it. Encrypt your wallet in your Bitcoin program and GPG it too, so it ends up triply encrypted 
There is no practical reason to encrypt something three times.
You either have all the keys stored in the same place -> Results in the same security as just a single encryption or
you have the keys stored in different places -> Then going for a secret sharing scheme after encryption is the better alternative.
Either way, encrypting something twice, or even a third time, doesn't increase the security.
Yes, but at least in this case your chain is as stronger than it would be if you had done it with only a single tool, because as long as you use different passphrases with same entropy, the encryption chain is as strong as the passphrase used in the strongest encryption program from this chain. If all three programs are secure, the attacker would have to crack three different passphrases in order to get to your wallet.
However, if you use the same passphrase, the encryption is as strong as the weakest link. In this case, the weakest link is going to be your passphrase used by your weakest program.
TL;DR: Yes, encrypting triple times can greatly increase your security, although it doesn't have to.