I want to know how long exactly did it take for Donald Knuth to create/design the font family of CM? (please answer based on authentic references.) Did the designing process take more than 10 years while the system of TeX was being developed?
In the preface (pp. vi-vii) of "Computer Modern Typefaces", Knuth sketches a time line that says he started work on the fonts in 1977, that he had produced "several hundred specimen sheets" by 1981, and that development went on during 1982, 1983, and 1984. The preface is dated "February 1986", so I think we can conclude that the design of fonts was finished by then.
But since then there have been occasional tweaks and improvements added. Most importantly in 1992 a revision of several characters, include the lowercase Greek delta, which Knuth has commented on.
In that comment he says: "These fonts are never going to change again". But at the front of my edition of the book it says "includes all corrections known in 2011". So I guess you could say that they have never actually been completely "finished".
There is a comprehensive list of references at the end of the Wikipedia page about Computer Modern.