Wood – What to look for in wood selection when building a coffee table frame with glass top

You have a difficult problem on your hands my friend. there is no way to remove oil based stains, including olive oil, from natural wood. Pine is actually a very soft wood and easily absorbs stains of all types. A very shallow stain can sometimes be steamed up, sanded and refinished, but a larger stain from an oil may have penetrated deeply into the wood fibers. The first method will not please you, that is to completely sand the table top to unstained bare wood and start the finishing from scratch. (see my previous answers of finishing pine) The second method may not be as successful in creating an even matching color, but maybe worth a try. Lightly sand the yellow area and feather into the unaffected area a little bit. Try to remove as much of the yellow as possible without making a divot in that spot. Custom mix some Minwax stains so to create as close a match as possible. Apply some of your mix to a scrap piece of pine, let it dry a couple of hours and compare the color to the existing color of your table. More than one coat of stain on the test pine may be necessary to get the depth of color to really compare to the original. This is obviously a trail and error method and a bit of patience may be required. If your color looks close but a bit too dark, use neutral stain to lighten it, if too light, use a bit of a dark base like ebony or a very dark version of the primary color. Obviously you need to know what basic color you are seeking, ie: maple, oak, cherry etc. and start with that base color and start experimenting. The more you can feather the replacement colors into the existing colors, the less obvious the repair will appear. Since the age of pine and cut of the wood, (heart wood vs outside cuts near bark) can make a difference on how it reacts to stains, test your best match on a very small area adjacent to some original color to check the match. You can use a Q tip and just do a small spot. Sorry I don't have a quick and easy silver bullet fix for you. Good luck

1/4" tempered glass should be fine. It's considerably stronger than the same thickness of normal glass, and also much safer in the event that you do manage to break it.

LED (or any other light source) into a glass sheet is normally injected at the edges (the LEDs being built into the table frame) - but it may not be all that exciting on a clear glass sheet (the ones you linked to were heavily textured - it needs to at least be frosted on one side for much light to get out.)