Please see my comment for suggestions to get a more informative answer.
How to save the output in a blockchain (on-chain) through transactions?
You pass a signed transaction to a function that is designed to receive the data (arguments) and you store the values in contract state variables.
How to include the On-chain blockchain in all this through transactions?
It's not clear that you need to unless a participant needs to be able to verify information another participant presents and/or the data in IPFS. A popular way to validate documents in IPFS is to store their hashes in a contract. Such a contract can also record the account that signed when the hash was first presented and it can limit access to authorized writers.
I can’t sign all my transactions with one private key
Yes. You can and you should sign all transactions from a given role or logical user with the same signing key. You use their address to authenticate users and addresses are usually the basis for access control.
I cannot generate several transactions in a unique smart contract
Actually, a single signed transaction can generate many things, or you can invert control and have a client iterate as needed. However, I would discourage storing the whole cluster details if that is what you have in mind. A single summary (32 bytes) should suffice. It depends on what you want to do which is not clear.
in a smart contract I can’t generate external transactions
This doesn't mean your application isn't viable. Only that you have not adjusted to the way to think about blockchain designs. We can probably provide a hint but will we need to know what you need to accomplish to suggest better implementation details.
Hope it helps.