Hi Cuban, to try and answer your questions:
The standard speed limit below FL100 is 250 kts, except in the specific circumstances you have stated which are also specified in our Manual of Air Traffic Services Part 1 (MATS pt1) which is essentialy the ATC bible.
Transiting from class A to Class D - if ATC say no ATC speed restriction then there is NO speed restriction, you can basically fly at whatever speed you deem necessary, we as "guardians " of that KNOWN TRAFFIC environment can de-restrict your speed.
Class E airspace whilst controlled airspace is NOT A KNOWN TRAFFIC ENVIRONMENT as VFR flights can happily transit through that area of CONTROLLED airspace without speaking to an ATC unit, therefore the SEE AND AVOID principle applies, hence the requirement for 250kts. However if you are flying through class E airspace and ATC say No Speed Restriction, then the 250 below 100 STILL APPLIES.
As for departures, the 250 below 100 is published purely for separation standards against traffic departing ahead of you. This is based on a departure table that tower controllers use, for us at EGPF it is designed to provide 5 miles constant or increasing separation between successive departures when 30 miles from the airfield following the SID route. If you are told no speed then the separation will be provided by other means, either there is no traffic likely to conflict, or your aircraft performance is such that no speed restriction will result in vertical separation from any conflicting traffic well before the 30 miles.
I heartily agree that this issues are not understood by many aircrew, as a controller working with Class E airspace, I am often amazed at pilots lack of appreciation of the rules and I'm sure that the majority don't even realise that they are in fact in class E airspace and just assume that a Radar Control Service means that we know about everything that is flying around. Unfortunately that isn't the case.
Thankfully posts like yours are promoting discussion amongst aircrew who are then taking the time to go and visit the ATC units concerned and have that cup of coffee and the chocolate biscuits that are always available for our visitors.
I've been lucky enough in my career to have spent many happy hours on the flight deck of aircraft and discuss the problems that we as ATCO's have and your requirements as pilots. This mutual appreciation of each others difficulties has helped me no end and I'm glad that slowly but surely controllers are being welcomed back on to the flight deck and more and more aircrew are taking the time to visit ATC units.
Only through mutual understanding of each others problems and needs can we make the skies a safer and happier place to be.
