Yes, the best way to do these things is to just go and deal with the consequences afterwards. Nothing like playing the innocent tourist who can't communicate.
I gave up a long time ago trying to ask permissions to do things because when in doubt, the usual policy is to say no. Much simpler to apologize after the fact and pay a little "fine".
As to the times, top men under three hours, women and old guys 3:30 to go up and down. In some ways, it's just as hard doing it in two days, many people are quite sore the second day and the first time I did it, I wasn't impressed with getting up in the middle of the night for a sunrise that never came. On top of it we left later because I knew it would take about half the time they said but we were passing or getting stuck behind tons of slow people. Between the choice of seing a possible sunrise with loads of people and being by myself on top with clear blue shy in the middle of the day, I choose the latter...