Yes, candra is a Sanskrit word meaning the moon, and is probably related to the Indoeuropean root of English "shine".
kalA is a Sanskrit word of unclear etymology which means a bit. (It also has the meaning art and a few others, but I do not know the relation between these meanings). In particular it often means the 16th part, so chandrakala is about the amount the moon's crescent changes in a day. From this usage, the lunar crescent on the day before or after the new moon, or a similar nail mark, is called candrakalA.