Hi, I've actually been in Italy for the olive harvest, so can make some pretty educated guesses.
Ripeness: dark-green brown, a touch squishy, but nothing like from the can
(this may have been the variety we were harvesting. to my knowledge though none turn black. that's a part of processing)
They do NOT taste good off of the tree. this is no indication. they are not eaten raw.
They also ripen all at once (ie for harvest we just put fabric down around the tree, picked olives off and let them drop, then gathered the fabric and poured the olives into a tote).
To do: The italians eat them cooked with pasta (surprise!). Alas, I never watched the kitchen closely
enough to see if there was some soaking/salting, etc. My Guess is that they are boiled and then added to the dish. They have huge pits that are daintily popped out of the mouth and set aside
Olive oil? I've never seen any home-processing, but I was in a region where there was a huge olive oil factory a short bike ride away.
I'm curious: what region of the country do you live in and what variety of olive are they? I've just never seen olives on a tree in the pacific northwest, YEt.....