Does the person I send the contract to have to pay to sign?
No, the person receiving the contract can sign it for free. All they need to do is create their free account, and that's it.
And in 20 years? Will I be able to verify the validity of my signatures as technology evolves?
Yes. Even if new standards emerge in the future, contracts previously signed on Flou will remain valid and legally binding. You will still be able to prove their authenticity.