Will Logseq remain fully open-source in the future and will the synchronization feature be self-hostable?

Regarding (1):
I see that Logseq uses AGPL license. Which should be even more strict about open-sourcing the code than the MIT license (if I understand correctly). Hence there is no need to worry about this aspect … correct?

Correct, because it is copyleft. All derivative works must retain the same freedoms as the original, if I’m not mistaken.