What linguistic process is illustrated by changing /a/ into /e/ in inars/iners? Assimilation? Why has it taken place?
This is called vowel reduction. Basically, a vowel that loses emphasis becomes weaker. This is very typical with one-syllable prefixes: ars > iners, facere > efficere. It can also happen due to inflection, as in tango > tetigi (from stem tag- with nasal augment in present stem and reduplication in perfect stem).
Old Latin had initial stress and therefore prefixes move stress away. When stress is lost, a short vowel tends to become weaker. The stress system changed later, but the vowel changes stuck.