In the real world it is unlikely that ATC would issue a late clearance as the pilot would request lower. Which incidentally I often do, but that is probably my bad flight planning. As to what point they are issued to increase or maintain speed I am unsure but now it becomes relevant I will take more notice. But aircraft that have entered Dublin controlled airspace are often requested to increase or maintain 300-310kts for spacing (and this can be as low as 3000ft) and are asked to inform when they need to slow. Pilots also frequently ask to maintain high airspeed or to increase airspeed to lose altitude more quickly. I suspect this is because approach often give the aircraft shortcuts to the localiser which results in them being high. A normal approach can be very convoluted. see charts. ATC also when asking if the pilot would like a shortcut tell them they can increase speed to lose height if they need to. I am not a real pilot and so don't understand the physics I just observe what is said. I listen to Dublin most nights as it is legal in Ireland to listen in.
Starting with your last point. It's illegal to transmit without an RT licence. Nor is it illegal to own an airband radio receiver. You can always plead to the court that you overheard a transmission! Many many Moons ago I was once stopped on top of terminal 3 car park at Heathrow by a police officer because I was listening. I produced my various licences including my RT licence and he had to walk away. I was actually more qualified to listen than he was!
I do find it unusual for an ATC unit to regularly practise something that they have published must not be done. i.e. they have published speed restrictions. To fly at speeds of 300-310 kts as low as 3,000ft is extremely dangerous for everyone concerned to put it mildly. It takes a good 3 miles plus to slow down to a safe manouevering speed from 310kts even with full on speed brakes, possible reduction to idle thust (which at that low altitude is also a high risk) So ATC are asking for trouble in that the number of airmisses would be very high.
You wouldn't be asked to "increase airspeed" in order to loose altitude more quickly. That's a highly dangerous manoeuvre. It means diving! The correct way to loose altitude quickly is to slow down to just above flaps 1 speed say 210kts and then full speed brake. The a/c will drop like a stone.
In the VC10 flying at 310kts at 3,000ft I am only 20kts below Vno. And the 10 is a high performance aircraft!
Here is something you can practise in the sim. An emergency dive. Fly to cruise altitude and simulate a depressurisation failure. Correct recovery in most a/c is: mask on, throttle closed, speed brakes full up, wing over at least 60 deg in the direction of your escape route. As FL240 approaches start bringing the nose up to avoid busting Vne. If you go over Vne you risk the a/c breaking up. There have been a number of potentially unexplained crashes where the a/c initially dived out of the sky and crashed in pieces. A depressurisation failure has been put forward in those cases as a hypothesis where the crew failed to recover the a/c from the initial dive.
Winging over in this context prevents negative G and consequently avoids passenger vomit down the back of your neck!