Yes they can, and commonly are (which is as annoying to ATC as it is to you).
Yes, but the only reason (that I can think off) for ATC to ask for the delay is because you started outside of the parameters. It's done differently in different places though, where I work we wouldn't approve startup outside the flight plan time. In Sweden I believe start-up is normally approved along with the clearance?
Where I work, not really, as we wouldn't approve it if the flight plan is outside the time. But it probably varies in different countries, maybe somebody who works in Sweden (or wherever this was) can clarify further.