1.Would you tell me if the steps I applied in writing out adjectives are correct or not?

a stone-accented conversation piece -- I don't know what a "conversation piece" is but I think it is something you sit on or use when having conversation with others.
First, I think 'conversation piece' goes together.
The "stone-accented' needed to be hyphenated since it goes together - meant to be one compound adjective (if that is the right term).
So, overall, the phrase looks to be correct.

I think you can add something like 'thoroughly stained' if you need to, making it:

a thoroughly-stained, stone-accented conversation piece

Normally, I think you wouldn't hyphenate 'thorougly stained' if used in front of a noun but this is a different case:
a thoroughly stained (conversation) piece

2. Would you use two (or possibly more?? - highly doubtful in its possibility though) adjectives that end in "-al"? How would you rewrite it?

a organizational procedural document

Thank you.
1-- It seems reasonable.
2-- It seems awkward. A procedural document for an organization.
1. Your examples are almost correct grammatically - just get rid of the hyphen in 'thoroughly-stained.' A conversation piece, however, is not necessarily something to sit on while having a conversation. It might be a statue in the corner of the room, a piece of artwork hanging on the wall, or anything interesting enough to cause people to talk about it. I suppose if there is a really interesting chair in the room, it could serve both as a conversation piece and something to sit on, but usually this is not the case.

2. Two adjectives ending in -al that occur together is uncommon, but not necessarily incorrect.
An 'organizational procedural document' is a 'procedural document' that is organizational.
An 'organizational, procedural document' is a 'document' that is both 'organizational' and 'procedural.'