I created a GreenAddress wallet to store my coins during the August 1 and subsequent events. I have my PIN number and Mnemonic, but experts say we should have our private keys too. Is it possible using this wallet?
In order to spend your coins from GreenAddress, you need to sign the transaction and they need to sign it as well.
You set limits for how much you can spend from your wallet, and you use 2FA, so that they only sign the transaction if it complies with what you have allowed yourself. This prevents an attacker from stealing everything in your wallet.
However, last time I checked you can't export the private keys from GreenAddress. While your funds are quite safe in general, they might not be handled properly during the chain split on August 1st.
And is really necessary to use that 2of3 account and nLockTime features?
If you want security in the scenario that GreenAddress stopped providing their service, yes.
Is my money safe by using this wallet? (Please, don't tell me to download a desktop wallet because I have no way to do it).
Your forked coins might not be. Ideally, you would have a wallet that lets you export private keys, and I
don't think you can do this with GreenAddress. As web wallets go though, it's pretty good.