2. This word is derived from "мера"="measure" and it can be literally translated as "measured (in all length or all directions)". Real meaning is related to this concept: you can translate it as "systematically", "without rush (because masterplan exists with all the details)", "monotonically", "sequentially". It can be also used to characterize things like dancing movements: well-studied, smooth and experienced.

1.ii "этим мир интересен" literally => "this is why world is interesting". Second particle "и" is used to emphasize verb. So we have "and this is why world is interesting"

1.i It's interjection very similar "Well,...", "So,...".

1. "Каждому своё" is direct translation of classic latin idiom https://en.wikipedia.org/wiki/Suum_cuique