I don't know with certainty about the first 2 questions.
I personally wouldn't use a stone carving with a polish that I was not aware of what the coating was. I hear some clear epoxys and resins are safe, but not sure if that's what you have. Also make sure the stone itself won't affect your water parameters, particularly in terms of ph and kh.
One test I have used on all stone items is to take the product "ph down" and pour some on the rock to make sure it does not fizz. At least then you have some idea of whether or not it will raise ph, which in my case is a concern.
As far as driftwood from the ocean, I am not sure how to get all the salt and minerals off. Perhaps someone with more experience on these 2 matters may chime in.
But the filter is a pretty easy fix at least! :) I use these on my HOBs
But you can find them cheaper at your LFS. Otherwise other brands aquarium filter sponges can be rubber banded or somehow tied to the intake. You intake looks like it may be smaller than the edge filter so you may need to modify it to fit as well. I find that just by sponging the intake it definitely slows down the current as well.
Good luck on your projects. They sound intriguing!