Do you keep all tributaries the last Emperor had? And how do you reform out of it? And how does that Catholic event works with the Mandate, would a Catholic Ming lose the Mandate?
Tributaries will only transfer if the target nation is annexed. A sufficiently weakened nation however, will find their Tributaries no longer seeking their protection.
The Catholic event still exists, and it is possible to switch and maintain the Celestial Throne
What happens if current Emperor would be wholly destroyed with non-claiming-mandate cb (let's say by european conquest)?
I like this question a lot, because it gives me an excuse to post this (ignore the placeholder event image).

The Celestial Reforms themselves are standalone, there is no unite the HRE style Finale
Do meritocracy bring passive bonuses, like Legitimacy, Republican Tradition, etc.
Nice catch, Meritocracy affects spy detection chance and advisor cost, from -50% detection and +25% cost at 0 Meritocracy, to +50% detection and -25% cost at 100 Meritocracy.