Many experience new insights and greater clarity. When you think that your designated time is up, open one eye and peek at the clock. This won't bring you all the way out of meditation. If there is still time left, close your eye and continue. You can also set a watch alarm or musical alarm, or place a wind-up kitchen timer under a pillow.
Any time of day is good.
It is best to have a specific time that is your meditation time. At first, though, you may find it helpful to experiment with various times to see if one particular time of day consistently produces more enjoyable meditations. If you are having trouble finding time to meditate, do it first thing in the morning. The possible experiences when meditating are unlimited. All of these experiences are alright and perfectly normal.