Is the "this" the dusty granules on the floor? If so, you could put some plastic or fabric on the floor and run it up the brick a few bricks to create a barrier. That way you can determine if it's coming down or coming up. If it's coming down, the debris won't be under the barrier. If it's coming up, it will be under the barrier.

Thank you. I am pretty sure it is coming up from the floor. I am just not sure what is it.

It looks like ashes but I think that's a gas fireplace as I think I see a gas line. But at one time it looks like it was wood burning so there may be some old ashes someplace. Do you have mice? They are wicked bad this time of year in my climate as they try to come in from the cold. A mouse can get through a tiny, tiny opening and could be stirring up old ashes as it travels into your house. Have you seen any mice droppings anyplace?

Is there moisture getting in behind the brick? You have efflorescence. It looks like something is dripping down the brick.

And this is inside the house?

Looks like frass.

There wasn't a Chimney cap up there when we bought it a month ago. We just got one installed yesterday. Do we need to get anything done to strengthen the mortar?

Did the installer notice cracks in the mortar that seals the top of the brick and around the clay flue? Cracks are very common there and need to be sealed with a caulk that adheres to mortar. If all obvious cracks are sealed then I would give the bricks a couple weeks to dry out and see if the mortar dust disappears. There are products that can clean the efflorescence off the bricks and mortar.

With 100% certainty it is not coming up from the floor tile, and if it was coming up from the tile it seems to be changing color in the process to match the color of the brick mortar, but again It's NOT coming up.

You have some serious problems with your chimney and urgently suggest you have a qualified mason examine the structure. You have a potentially dangerous situation right now which needed addressed ASAP so read and understand what I'm about to tell you.

• The Corbel bricks holding up the stone mantel have lost most of there mortar and is at risk of failure bringing down the mantel and half the face bricks on the front.
• There is excessive moisture getting into the chimney from the top. You say the Cap was replaced and the term cap would refer to the metal cover above the clay flue liner, but the Chimney CROWN (see picture) needs examined and a main reason water gets into a chimney. (see picture)

• The Crown could just be caulked if damage is minor like a few cracks but based on the condition of the brick mortar on the inside it's likely to be more severe and need replaced.
• based on the condition of the inside bricks I also expect the bricks above the roof line to be in much worst condition and at the least need tuckpointing or even serious enough to remove and rebuild the bricks before a new crown is built.
• The inside is in serious need of tuckpointing but the whole thing needs inspected and assessed to see if It's even worth the expense to repair. So get someone to look at this accident ready to happen ASAP.
• If the crown and /or the bricks above the roof line are shot it can be wrapped in plastic to avoid moisture to enter until repairs can be made.
• DO NOT use the fire place! The clay lining also needs inspected and if they are cracked or have bad mortar joints the smoke can come through the cracks of the liner and the deteriorated brick joints and into your house.

This is serious stuff you're into and dangerous to ignore.