how to clean old wood stool?

Use a damp cloth first. Wipe away surface grime and dry it immediately with a soft towel. Water damages the old finishes if left to soak into the grain. Apply a clear beeswax polish once or twice a year. Buff it with a brush to protect the timber and maintain the patination.

My grandmother had this heavy three legged stool in her kitchen for years and I want to know if it is safe to use as a step for reaching high cupboards?

Most antique country stools were built to hold heavy human weight. The wedged joints remain very strong when tight. Tripod bases are designed for seated balance rather than standing. If you stand near the edge of a tripod seat, it'll tip over. They work well as occasional seats but pose a genuine risk if used as a step ladder.

what kind of wood is my milking stool?

Look closely at the grain pattern on the seat. Elm is a common timber for the tops because its interlocking grain stops the board from splitting. It often has a wild swirling appearance. Legs are usually a different timber. Ash or oak were chosen for their straight grain and rigid strength. Mixed woods are standard for these practical pieces.

The legs on this small wooden stool are wobbly and loose when you sit on it so can I just put modern wood glue in the joints to fix it?

Modern synthetic glues ruin traditional joints. They dry brittle and prevent future repairs by sealing the wood fibres. A better approach involves removing the leg and replacing the wooden wedge. This expands the original timber back into the seat hole without chemicals.