Hi – sorry you’re experiencing difficulties.
Yes, your data should remain intact, but we’d always recommend making a complete backup (and knowing how to restore it) as a sensible precaution 🙂
To the problem at hand, it looks like requests to load the next/previous month are being redirected, so that they use the secure HTTPS protocol: I’m curious, could this be because you have a security or SSL helper plugin installed, or due to some configuration setting?
Can you confirm the problem was still present when you removed all other plugins and switched to a default theme (I realize you indicated having done this, but I’d like to double check as what I’m seeing isn’t the expected behaviour on a clean WordPress installation).
Let me know how you get on!