Paragraph (a) bears repeating: (a) In the event of an engine failure caused by a major mechanical fault (e.g. seizing bearings due to loss of oil), the rate of deceleration of the engine can be rapid and it is thus imperative that the pilot take immediate action to feather the propeller before the rpm falls to the 1000 rpm region.
In the case of Piper aircraft they usually include the minimum feather RPM in the checklist for feathering, as well as a description of it in systems. It would be very worrying if instructors today are not teaching this, as its vital to understand what the feathering locks are and how they operate, this in additional to how the prop control mechanism works, oil flows etc. I remember it used to be emphasised during the full feather demonstration where we would shut down the engine in flight, fly around for a while single engine to get a feel for it, do a restart, and in ages long gone, shut it down again and land feathered. Even if you are adverse to feathering engines you should do a sequence of simulated single engine flight at zero thrust including level, climbing, turning, climbing turns, to see the performance and how it can be improved.
From memory in my training it was something like 300ft close the throttles landing ahead, above that and blue line then feather, and when above something like 1500ft continue the drills for basic troubleshooting.
As for knowing the speed specific for the weight, again if memory serves, in a light piston it is only a variation of some 5knts.
Years ago we used to practice engine failures at 200ft (some lower than that) after take-off by cutting the mixture, ie you had a real failure, you would then climb away on zero thrust at blue line to circuit height to prove the aircraft can do it. All my training was done this way in everything up to a Navajo, mixture cuts included (not advocating mixture cuts but just that its is an actual failure, if you don't trust the throttle method actually replicates a failure). You should be close to blue line if not above by 50ft in most light twins, if not why not, by 100ft you should be above blue line and climbing away nicely. A PA-44 training is usually close to max weight most of the time anyway. Even most 6 seaters these days are only 4 seaters with max fuel because of all the toys they carry, so 2 up they're only 150kg off max, chuck in a little ballast and you're almost there.
The key here is you have to make a decision once the runway runs out, can you make it, depending on a lot of factors you should consider before take-off. Above blue line, without sufficient runway I would be thinking "go", control, clean it up(drills), assess whether my performance meets my expectations. If performance satisfactory, continue the "go" plan, if things look ugly, use what performance I have to follow the "stop" plan (includes knowledge of likely landing areas, similar to what you would think SE.
This process must be 100% methodical and not rushed, but that does not mean its is a slow process and it should not be delayed in any respect at any point of flight if there is oil issues or anything affecting the prop mechanism or engine that could possibly cause RPM below minimum feathering. On take-off the initial actions should already be complete, everything is just a confirmation 10-20 seconds and you are ready to feather, rushing will only save a few seconds that may lead to big mistakes and in the end will not change the outcome.
If you are on approach feathering is the least of your concerns, just add a bit of power to pick up the slack of the dead one, bit of rudder and the aircraft will not know the difference. Go arounds are another can of worms as Centaurus mentioned.
Where I've seen most cause for concern is engine failures late final, usually requires a good deal of power to overcome the loss of power and windmilling prop combo. If you have time I would always recommend identify and feather the dead, there's always a chance you might not have the performance to make the field from above 200ft on final. There are also a lot of accidents caused by pilots choosing not to feather and having to suddenly add power late final and losing control. It's also important to still follow the drill, without getting too distracted from flying, control, mixture, pitch and power up (to maintain glide path), then you are almost there to identify & feather anyway. In some aircraft in a descending turn at low power you can get the aircraft to yaw towards the live engine, if you follow the drill and power up it will remove any false yaw.
I also remember one pilot who had an engine failure turning final, he was high and fast, elected to do the drills after the turn to final complete and found he'd pulled a mixture back with the throttle (Beechcraft), power restored and now a normal two engine landing resumed.