The answer is “yes” to both questions
Yes, according to ART. 25.2 eIDAS Regulation, a qualified electronic signature is automatically equivalent to a handwritten signature and has equivalent legal effects.
Yes, intermediation is required even when using a qualified electronic signature. This is not because it can be called into a question that the contract has been signed, but because of the uncertainty of the linkage with the content signed and all the evidence of its availability in durable support prior to the signing.
The qualified electronic signature has various defined legal effects, which are the same for all the Member States of the European Union, given that the eIDAS Regulation is directly applicable in all the Member States. As a result, electronic contracting with a qualified signature is equivalent to the handwritten signature and can be used between companies in any country in the European Union.
The eIDAS Regulation does not grant legal effects to the rest of electronic signatures, but the member states have full freedom to define their legal effects. That is, they can be considered equivalent to the handwritten signature or not. However, in Spain, the usual practice with full legal validity is remote contracting with non-qualified electronic signature systems: operation codes sent to mobile phones (OTP’s), digitized handwritten signatures, or even advanced electronic signatures through third-party interposition services such as those offered by Logalty.
Logalty is currently working to go further and for this reason has been working in Europe the last two years as an active member of ETSI (European Telecommunications Standards Institute) participating and helping in the creation and definition of technical standards, specifically, those directly linked to an essential trust service whose conformity assessment is currently being finalized: “eDelivery”.