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Apparently this is common in Mazda vehicles (as per the dealership) and is NOT a fault that can be fixed but an "inherent harmonic". Google search is interesting! Does anyone have any suggestions or information on this please.

Is this an engine/driveline vibration or wheel/steering vibration?
It's not something we have experienced with the Mazda3 and not something that we have received complaints about, but would be interested to know more.
Also, is it the Skyactive engine?

Definitely not wheel/steering. It is not the Skyactive.
So far I have had wheels swapped front to back at service- no change; wheels balanced (I paid for this) - no change, service had the car for a day and a half to tell me a new rim needed to be fitted (assured this would fix it) - 2 weeks later the rim is changed - again no change;
So now a little miffed I arrange to show the Sales Mgr the problem and suddenly I am advised the vibration is an "inherent harmonic" and " this vibration is common in most engines and only happens at 2,100 RPM" (I have that bit in writing btw).
The car vibrates at 2100 RPM when it is stationary or moving at ANY speed (usually for my driving that's between 80-100kmph).

OK. I can't see why they thought balancing wheels or replacing rims would fix the vibration if it occurs when the car is stationary, or perhaps they misunderstood.
The problem with harmonics is that we're all sensitive to different frequencies and as I said, it's not something we have noticed on this model.
Has the dealer offered for you to try another similar car, just to be sure it's a characteristic of these engines? Unfortunately, if it is a characteristic that they all do, it's unlikely to be something that can be changed, however if other similar cars don't exhibit the same thing, then I would think something could be done about it.

The whole car vibrates. Everyone feels it, not just me. With the hood up you can see the engine shuddering. The service tech guy agreed on test drive with my husband that the vibration 'was not normal' and 'not coming from the wheels' - and this was PRIOR to them having the car for a day+ and determining the rim needed replacing!!!

Interesting that the technician said it's not normal and now theyr'e saying it's a characteristic of this model.
I'd still suggest asking them to let you drive another similar car for you to make a comparison. If the other car doesn't exhibit the same vibration, then it would seem your car has a fault - not a "characteristic".

not only a 'characteristic' of the model - 'this vibration is common in most engines' is what I have in writing. It does not apparently occur in the Skyactive System. I've never had a car (of any make or model) do this before.
Mazda Service have now replaced number 1 & 3 engine mounts. The vibration is now 'cushioned' better but is still there. So my guess now is that the vibration has been there since day 1 but steadily felt worse as the constant engine shake has worn out the other mounts (???). If this is likely then I assume the vibration is going to do the same to the new mounts. :( Could this be damaging other bits of the car that I am not aware of yet???
Do you know if I can get a 2nd opinion (not for someone to do ANY work - just LOOK to see if they have any ideas I can give to Mazda or the Dealership) without affecting my warranty?

Perhaps another Mazda dealer may be able to provide another opinion. The dealers are the ones who know these cars best, so may be able to provide more insight than a generic garage.