Are these bottles airtight? What is the cork made out of? Can they be used for storing alcohol and other volatile food products?

Please check same bottle with glass stopper. It has leak proof seal inside: http://www.amazon.com/Nakpunar-Spherical-Clear-Bottle-Stopper/dp/B01BZ3I4W6/ref=sr_1_4?ie=UTF8&qid=1456235475&sr=8-4&keywords=Nakpunar+spherical

Will it float if used for a message in a bottle?

Yes, it'll float. Just be sure that the cork is tightly closed and not take any water inside.

Could you tell me the size of the base (the flat part on the bottom)?

Yes, the flat part is exactly 1 3/4" inches in diameter. The bottle is 4" tall. It holds the 7.75 fl. oz or 230 ml contents of the Thymes Frasier Fir Reed Diffuser Refill that I put in it very nicely. Frasier Fir scent is awesome! 10 to 12 reeds in the bottle work beautifully to scent the area around a sink or toilet.

Is this glass food-grade and lead free?

I haven't used mine for food stuffs; so, I couldn't say. There are, however, listed as good for oils and salad dressings, which would lead me to believe they are food-safe. Sorry, I can't give you a definite answer.

Spherical Clear Glass Bottle, 8.5 Oz. w/Cork (1, Cork)

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