On the cup of tea: please do not, and the reason is worse than sticky keys.
The key block is directly above the key frame and the action. A spill there does not sit on the surface — it runs down into the mechanism, into felt and cloth and wooden parts that swell. Technicians will tell you that liquid in the action is one of the more expensive accidents an instrument can suffer.
A piano is one of the few pieces of furniture where the flat surface is genuinely not a surface.