gem stones are only good for selling. I found the best thing with the letters was to read them then leave them on the ground as they only take up room in your inventory. Tombs as far as I have observe don't have any real perpose, same with the necklaces. hope this helps.
1) These handfulls of gemstones and jewels are only for selling and have different cost according to their quality.
2) Usually notes have clues but you don't have to keep them, as for these books i think there are called Ancient City Records the only use i found is to sell them.
3) I found that strange too with these 2 items but they have no use for quests in the game.
"When I am working on a problem I never think about beauty. I only think about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." Buckminster Fuller