Am I getting this right ?
You can have one big transaction and pay just one fee for that big transaction BUT in that big transaction also have like 10 or more transfers of coins / secondary transactions too ?
Yes, but normally the fee you pay is proportional to the transaction size anyway.
Actually, this leaves me with a doubt too. What is actually signed by the inputs of a transaction? Is it the entire output list, or a constant size hash of such output list? Because if it is the former, I guess you risk using more space with bundle transactions, since you'd have to sign every output with every input.
Since signing is computationally intensive (and directly linear to the size of the digest) you sign a hash of the data. This applies to other forms of cryptographic signing than just Bitcoin. This is why security of hash functions is taken so seriously, if the hash function is flawed you can spoof a digital signature even if the signing algorithm is secure.
Signing: transaction -> hash -> hash signed w/ private key.
Verifying: transaction -> recreate hash -> sign hash w/ public key and verify against recreated hash.
