Attached to a transitive root, the suffixoid -iĝi detransitivizes it, this means the verb gets the meaning of a passive or of a reflexive: ruli 'to roll (something)' - ruliĝi 'to roll oneself, to be rolled, to roll (intr.)'
So fariĝi means 'to be made into something' or 'to make oneself into something'. There is a slight difference in meaning to mere iĝi, which means 'to become' (without an overt causer), but it will be hard to find a context where this would be of importance, especially as fariĝi may also be generalized to an extent where it means 'to become' without thinking of any causer.
With intransitive or stative roots like esti 'to be' iĝi means 'to become': sidi 'to sit' - sidiĝi 'to sit down'.
So estiĝi means 'to become being', which is actually identical to 'to become'.
You ask why in such cases there is a root before iĝi at all, as they don't add real information. This has historical reasons, as in the early stage of the language the affixoids were used as standalone words much less often than today, certainly by the influence of European (and other) languages, who don't know affixoids, but much more strictly distinguish between standalone words and bound affixes. The evolution of the "liberation" of affixoids in Esperanto is a slow process, for instance suffixoid isto 'professional' still today is hardly used as a root.