I would suggest you run some experimentals with the wood that you intend to use for your projects.
Copper has a pretty high melting point and pours like thick honey.
Aluminum has a much lower melting point and pours like milk.
How do you intend to melt the metals ??

 

I was going to buy a crucible melting kit from Amazon but even at an affordable price I’d rather know if it would work first before purchasing. No point in wasting money, can’t see me using it for anything else. If it did work then it opens up a whole lot of new ideas like filling in small checks, holes on live edge slabs, table leg designs and even geometric wooden art.

 

Yes it would burn. You should expect the wood to be charred around the pour and once cool the metal would fall out because it wouldn't adhere to charred wood. I've poured lead which melts at a lower temperature into the head of a mallet. I leave enough room at the top which I can insert a wooden plug in behind it to hold the lead in.

 

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you can get some good (and bad) info off YouTube. You don't need to buy a store-bought crucible. I'm in the process of building a Propane Tank Foundry (BBQ size tank) and have a couple of crucibles made from the smaller hobby size propane bottles which can melt aluminum in a charcoal fire with a hair dryer blower taped to a metal pipe. (it ain't rocket science). As with our own Safety Warnings, you must excercise your own best judgement and use the appropriate personal protection equipment.

https://www.youtube.com/results?search_query=propane+tank+crucible

 

Use a small router with a 1/8” bit, route the path, and then pound some #8 solid wire into the groove.

 

++"yes it will burn"

Similarly, I have some art made by a glass blower who while shaping his work drops it on pieces of driftwood and that burns the wood...I have to believe a molten metal would do the same.

 

To the First Nations of the Pacific Northwest, copper is a mark of wealth and prosperity. In modern times, there's lots of copper inlay but everybody buys sheet and uses something like a Delta jig saw or a Knew fret saw to cut the needed shapes.
All sort of metal sheet and precious stones can be had from places like Rio Grande Jewelry Supply.

 

Looking at the problem sideways.... cut the shape in a scrap piece of wood, use it as a disposable mould. Once cooled, throw the mould into the fire wood pile. Then trace the shape onto the piece you want to keep, and rout it out.
There is a "but" here, wood and metal expand and contract at different rates and amounts. You would need to use a 2 part epoxy to hold the shape in the hole, and expect a seasonal small gap to appear around the shape.

 

First Nations carvers in the Pacific Northwest very carefully undercut the rim of the inlay shape for the metal/glass/shell. As the wood of the carving dries, it shrinks a little to have a firm seat for the inlay.

The Sealaska Heritage Institute published a set of 3 paperback books: Tlingit Wood Carving. In the back of each one is a lavishly illustrated chapter on doing inlay. ISBN 978-0982578629 author: David Beasley (Deexwudu.oo). 2009.

I: How To Carve A Tlingit Tray
II: How To Carve A Tlingit Hat
III: How To Carve A Tlingit Mask