The oil will gradually float to the top and you may be able to draw it off carefully.
The color
yes
It depends on the type of stain you are using, usually the label contains the correct information, oil based stain generally takes 24 hours, water based takes less time, alcohol based takes even less time. If there is no label, it could be old stain and it might not mix well with your finish. your best bet would be to discard and buy new stain to match with your finish. (water based stain with water based finish, and, oil based stain with oil based finish)
Yes! Providing that the stain in question is "oil based"! If the stain is LATEX then no. Oil based products will mix, but oil and water won't! Water being the carrying agent of latex!
Yes you can if it is a solid stain. However, if you're using toners or semi-transparent stains, you'll want to remove all the water based product prior to applying the oil based stain, otherwise, it will appear blotchy if the water based stain is worn unevenly.
Generally, yes, although the water-based stain may run a small amount after application if the wood still has a lot of oil present in it. After 15 years, it should be okay.
Oil based stain is best on Brazilian Cherry.
You should check the label on the specific product you're planning to use. If the label states it will adhere to wood with an existing coating, then it's fine to use even over an oil-based stain. (This is because once thoroughly dried, oil-based stains behave the same as water-based stains.) Some products, however, will require the existing stain to be stripped from the wood, or to apply a primer coat over the existing finish before applying new stain.
Yes, you can
Depending on the stain technique it can take anywhere from 2 to 24-hours for the stain to dry. For cabinets, you should wait the entire 24-hours to make sure the stain is not still tacky and to prevent smudges on the finish.
By testing it with denatured alcohol. If the paint comes off on a rag soaked with the alcohol, then it is water based, If not, oil.
I am doing that right now. It says on the can that it can be applied over an oil based stain...but the stain may continue to "amber" under the coating. I decided to go with the polyacrylic because a friend told me that polyurethane yellows over time. I don't know if that is true...but that is what I decided to do. So far, the acrylic is going over and drying over the oil based stain without any problems.