"A quarter to nine."
From my experience, in Chinese you can say 差一刻九点 as well as 九点差一刻. Both should be correct (have reported).
I would prefer to say 8:45. It's really weird to say a quarter to nine in Chinese.
I don't think so. In ancient times, 一刻 means a snick in a device that measures time by the flow of water, not 15 minutes. Now 一刻 is a quarter of an analogue clock. Unless all analogue clocks have turned into dust, 一刻 will keep its place.