Unless you want the rocks to affect the water chemistry, the best test is to dump some vinegar on them. If you hear a fizzle,or see bubbles, it's not inert and will change the water chemistry.
Slate? - inert
Granite? - inert
Shale? - not inert
Fieldstone? - I don't think it's inert.
Flagstone? - will increase hardness
River rocks? - depends on the composition--river rock is usually granite.
Petrifiedwood? - inert
Pagoda? - no clue?
Lava? - may increase iron, and hardness. If it's 'real' lava rock, it will. They sell 'lava' rock that is a by-product of the smelting process, and it is normally inert.
As always, you can test any rock by determining the water parameters of a gallon of water, soaking the rock for a week, and retesting the water.