What makes us believe that the Cosmological constant was the same in the past?
And if there is no way to prove this then could the age of our Universe be different from the current calculated value since the Universe could be expanded at a different rate in the past?
Even if the Cosmological constant value was different in the past how are the fail-safe limits calculated giving a finite tolerance to the current prediction of the age of our observable Universe?
The time evolution of a universe in which the cosmological constant is actually a variable can indeed be modeled on a computer, and the results compared to observational data. If we imagine a finite-element expansion model where the time variable is divided into discrete slices, then for any time slice the CC corresponding is updated in the model with a new value and the corresponding difference equations are solved. In this manner the expansion process is clanked forward one time increment at a time with a different value of the CC used at each increment.
It is, of course, possible to add dynamical fields to the theory which act as Dark Energy given an appropriate equation of state. In general, different models will indeed lead to a different age of the Universe.
In addition to its simplicity and the good agreement with a large array of observations, the cosmological constant is well-motivated by Lovelock's theorem, which states that under a few reasonable assumptions, the gravitational field equations take the unique form
$$ a G_{\mu\nu} + b g_{\mu\nu} = T_{\mu\nu}, $$
with two constants $a$ and $b$. These are fixed by specifying the Newtonian gravitational constant and the cosmological constant. From this perspective, having no cosmological constant would actually be kind of fine-tuned.
