Why is Hikari's nickname "Pikari"?
In Japanese, Pikari (ぴかり) is one of the numerous mimetic words of the language, meaning "in a flash"/"sparklingly"/"brilliantly", mostly associated with thunder and lightning. (Also, Hikari itself means "light", but I don't really know if it's related or not.)

Given the energetic and cheerful nature of Hikari, it's a fitting nickname.

Some references :


https://en.wikipedia.org/wiki/Japanese_sound_symbolism
http://jisho.org/word/%E3%81%B4%E3%81%8B%E3%82%8A