The lightening network could help you reduce the fees that are paid on transactions, considering that you're expecting multiple transactions with a lower amount.
I calculated already with an online fee calculator, and the transaction fees currently would be ~10% of the actual value.
This is wrong. The transaction fees depends on the ferrate at a particular time as well as the size of the transaction. It has nothing to do with the value of the Bitcoins being transferred; would be quite absurd to pay $100,000 for a $1 million worth transaction.
Is it possible to send without any fees? Or less than 1sat/bit?
You can technically create a transaction with no fees, but the chances of it getting verified by the nodes or confirmed is almost impossible now.
Lightening network reduces the fees significantly though.