dynamic - InputField as both in- and output fields with ContinuousAction

Many years ago, I made a handy little program in Flash.

It consisted of a number of input fields, each representing a variable that was dependent on all the others. As soon as any field changed, the other followed, no matter which of them I changed.

So they where effectively both in- and output fields.

A simple algorithm kept track of which field would output the result, (usually the one which had experienced no change or with oldest edit).

EDIT: Only one variable is calculated each time a value is changed.

It may be partly exemplified by the following code. However, in this case only the last InputField "c-variable" is calculated, while the goal is to arbitrarily be able to chose which is to be calculated. The latter can be achieved either by a checkbox or algorithmically.

    Clear[a, b, c]; Row[{Labeled[
   InputField[Dynamic[a], Number, ContinuousAction -> True, 
    FieldSize -> Tiny], "a-variable", Top], 
  Labeled[InputField[Dynamic[b], Number, ContinuousAction -> True, 
    FieldSize -> Tiny], "b-variable", Top], 
  Labeled[InputField[N@Dynamic[c = (a*b)/2], Number, 
    ContinuousAction -> True, FieldSize -> Tiny], "c-variable", Top]}]

So my question:

Is there a simple way of programmatically switching the properties as to make any arbitrary field an output field?

Another question comes into mind: The exemplified InputFields above can't handle backspace. To change the first digit one has to double-click. How could this be accomplished?

EDIT 2: I have answered some of the points in my answer below.