Wezzy, you can get the letter to Tifa if you play the piano in her room if you have Tifa in your party after you have got Cloud back. You also get something else along with the letter, it's what people usually play the piano here at all for, the letter just offers some explanations. If you play it on the 2nd disc before Cloud returns, you'll get an Elemental materia.
And about the waterfall.. somewhere between Corel and Nibelheim, there is an almost completely round lake, surrounded entirely by mountains. You can only get there by Chocobo (green, black or gold) or by submarine. There are 2 underwater caves, one leads to the key to the ancients, and the other leads to that round lake. By the lake there is a waterfall, just run into it and you'll enter a cave behind it. You need to have Vincent in your party. After you're done, exit and fight ~10 battles and re-enter, again with Vincent in your party (if nothing happens, fight a few more battles and try again). You should get something (not telling you what
).