This article will help with when to harvest (go to the bottom half of the article): https://www.gardeningknowhow.com/edible/vegetables/squash/when-to-harvest-squash-best-time-to-pick-winter-or-summer-squash.htm

The squash can be stored in at room temperature in a somewhat cool and dark location, like in a basement or pantry, for about a month. Keep it dry.