You can submit your own art, but the coin will be more ‘accurate’ if you have final art completed PRIOR to minting. (in other words, if I wasn’t an artist I dont think I would rely on the mint for my artwork – they are all over the place)
Start to finish – depending on number of coins – it varies. Is the coin round? 2D or 3D, how many colors will it have? Etc, etc…
I would EXPECT to spend around $1500 for your coins (Could be more, could be less) The market is good for a well-designed coin, and personal coins usually do fairly well. (As long as the coin is done well)
The time it takes depends on the mints art usually! Sometimes when you send over art, they just cannot get the blueprint right. I had one coin take 12 tries to get correct. After THAT is done, it takes about a month.