Discontinued Content in 2.0

[Raldo]

Lets see...

This covers Lodestone history (vaguely)

In A Realm Reborn, the date on which an achievement is completed will be recorded as part of an in-game character history, which will be maintained in a manner different from current character histories on the Lodestone.

and this covers in-game achievements

In A Realm Reborn, you will be able to check the achievements that you completed in the current version and the amount of points you received will not be lost.

The titles/rewards likely will remain on your character; it would be quite silly if they didn't. I think the covers most/all of your concerns.

That said, achievement points don't actually mean anything, and I find the concept of meaningless points to be quite absurd. I wish you could spend achievement points or something. You won't find me wasting my time doing those behest/levequest achievements, that's for sure.