Installing a shelf in the bathroom

Pull the toilet a look down the drain pipe. You should be able to determine what elevation the drain is running at, as well as what material the drain is made of. Both of theses will help provide you your answer. You'll need to buy a new wax seal for when you reinstall the toilet.

It’s hard to tell from the pictures how thick the bench is. If it is 7/8” thick or 1-1/2” thick. It may be just the perspective of the picture but those screws look smaller than you described and the drill bit looks bigger than 1/8”. It seems you did everything right although the glue was probably unnecessary. The screws really shouldn’t have stripped out like that although the screws may have been a little short. I would use as long a screw as will almost go through to the other side. I would also use as thick a screw as will fit through the holes in the metal plate. Alternatively even better, I would drill all the way through the wood with a bit the same size as the holes in the metal and use bolts and nuts. Again as large as will fit through the holes in the metal plate. On the under side use washers and lock washers.