1 - At the moment, we don't. :( One of the next things we'll be working on is an end-to-end encrypted cloud sync. So we won't storing the "raw" thoughts, but you'll still be able to get access to them.
2 - Ah, our reminder notifications kind of work like that, but we'll probably try to make that more configurable as the days go on.
1 - DayOne (and to a lesser extent 1Password) had problems from this. Both supported Dropbox initially which was great for privacy-conscious users as it was user-controlled sync, and easier on the company as they didn’t have a server infrastructure (or much of the accountability). They’re both now pushing for sync to their own cloud (helps drive the subscription model) and it’s starting to show if you look at the behaviour of those same privacy-conscious folks.
I think it may be a mistake to move to “trust our black box” cloud sync in your case as you’re asking trust of the very people who in some cases have feared trust backfiring for their whole lives.
2 - Ah, our reminder notifications kind of work like that, but we'll probably try to make that more configurable as the days go on.