Since the beginning of Web3's talk I started wondering whether it's possible to build a fully transparent and open source platform, one where not only we know what data is saved but also can see the data itself. Would there be a way of doing this without breaking all privacy's laws?
Yes. Start from an open processor architecture and one of the open toolchains, use the open subset of an OS. Storing other people's data on it is still subject to legislation (I assume, but would verify, that storing your own data is fine).