I think you probably have a metamorphic rock. From what I can see in the pics (thanks sssooo much for including those, makes this much easier) the white is likely veins/striations of quartz...buuuttt, to be sure, take a steel knife and try to scrape off a bit of the white stuff, see if you can make a powder. If you can't, they are quartz. If you can, put some vinegar on the powder to see if it fizzes (VERY important to powder it first!)
If the powder fizzes - the light bands are calcite or dolomite. These are calcium minerals and will potentially raise the pH in your tank. However, the amount of these minerals in the rock is extremely small, and if you're doing regular water changes it likely isn't going to affect much as you'll be removing it as fast as it appears. Unless you've got extremely delicate fish I wouldn't worry.
If the powder doesn't fizz - likely clays. Inert!
aquascape away!
I think the black stuff is either chert or metamorphic minerals like biotite and possibly amphibole. Also inert.
Rocks get transported far and wide and are often found very far away from where they were formed, so where you found it is SOMETIMES a good indicator of what it may be, but not always.
The ring in your sink? dirt.
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