The Ran in Maseches Shabbos 9a of the Rif, s.v. אי נמי לשיעורא, cites a dispute between the Rif and some of the Geonim about your second question. The Rif held that after the time period of the mitzvah has passed, one could use the light, or take some of the oil. The Geonim disagreed, at least about taking the oil, and held that even if it went out on its own, you should save the leftover oil for tomorrow's lighting. The logic which the Ran brings for their opinion, namely that the entire volume of oil is dedicated to the mitzvah, should similarly prohibit using the light.
The Tur and Shulchan Aruch in Orach Chaim 672:2 go with the Rif. The Mogen Avrohom there #4 brings the opinion of the Maharshal that one may extinguish the flame but may not use the flame if it remains lit (because someone who sees you using the flame won't know how much time it has been lit). He also cites the Bach that both using and extinguishing are forbidden.
Mishneh Berurah 672:7 writes that if one wants to extinguish it after the time has elapsed, he should make the explicit condition that he is only apportioning for the mitzvah the amount of oil necessary for the mitzvah. In 672:8, he cites the opinion that one should not use the flame while it remains lit.