I used to use screws too, but I discovered that for small projects glueing is very adequate if done properly. For scroll saw projects I use Aleen's tacky glue. I apply a very small amount to one surface. Using a toothpick, I spread the glue to make a very thin layer while removing excess glue. Mount the two pieces together pressing them together with a slight twist. Then with a clean toothpick, I scrap off any excess glue before it dries. I have been doing it this way for years and have never had a failure.
As far as stain, I never stain! I always use hard woods which usually impart their natural color when oil is applied.
I do not reccomenc using mineral oil though. While it is reccomended for cutting boards and utensils, it is not for plaques and such as it never fully dries and could stain furniture. Always use products designed as a finish, mineral oil is not.