What checks do you need to carry out to make sure tools and equipment are safe to use and in full working order before starting the activity?

for hand tools, check for cracks or deformations like on sockets make sure there is no cracks in the side of the socket and that the inside of the socket is a clean 6 or 12 points (not rounded) and the 1/4, 3/8, or 1/2 inch square on the other end is in good condition.

wrenches shouldnt be bent, the open end's sides should be parallel, the box end shouldnt be rounded out on the inside, and again no cracks etc.

jacks should not have any leaks and be able to lift to their highest position (if it cant its probably low on jack oil). You should also have jack stands that are not rusted or bent and have no cracks in the metal. You should use said jack stands instead of rely on a jack to hold the vehicle up.

basically just make sure everything is in good condition, not damaged, not rusted, etc.