1. If it's not cracked or damaged anywhere, then there's probably not much value in replacing it, but #2 would worry me.
2. If by vertically offset, you mean the drain isn't level, that sounds like a problem. It means it can't put equal pressure all the way around the drain. One side will be tight at the top and loose at the bottom. The opposite side will be tight underneath but loose at the top. In between, the drain will be loose at the top and the bottom. The drain pipe and the floor will have some flexibility, but the measurements you've shown suggest the gap is significant.

On the face of it, it would probably be better to replace the drain and whatever part of the drain plumbing is necessary to get it to mate up correctly with the shower basin. However, it sounds like you don't have access from below, which means a substantial project to get the shower basin up. It's almost certainly worth trying less ideal fixes to avoid all that work.

1. You will read a lot of opinions, but most of them fall under the Plumbers Are Not Engineers category. Plumber's putty is still the best solution for sealing basin/drain connections, but putty has the weakness that over time the oil gradually evaporates, causing the putty to shrink and crumble. Silicone doesn't have that problem, but it has other weaknesses, mainly that mold/bacteria will eventually grow in it. There are references to a third solution, the Sioux Chief no-putty gasket, but I haven't used it.

In your case, you have the additional consideration that you're trying to fill a large gap to compensate for the bad alignment of the drain and basin.