[Jelonna]

I believe the quality of the items you turn in effects your rewards...as well as the difficulty of the work order.

As far as which table, there is a refining taskmaster and a finishing taskmaster. The table you use will depend on which taskmaster you got it from. Also, a table will only show you the recipes you can make on that table; i.e. the finishing table won't show you refining recipes.

Some of those "you do not have all the items necessary" messages were bugs involving the game not recognizing certain tools. That error was supposedly fixed in the last patch, and I think it mostly affected artificers but keep your eye out for that too.