Day and Night Cycle
The sun is a stationary orb in directly in the center of the sky. During the day the sun is at a steady brightness. During sunset the sun will get progressively dimmer until it is night time. During the night the sun is dimmer than our real-world moon. When it is time for morning the sun will begin to get brighter again until it reaches daytime. The sunrise-sunset process takes about an hour.
The moon goes through different phases in a 42-day (1 month) cycle similar to our own world. When the moon is empty that signifies a new month. 8 months makes 1 year (336 days). The moon is barely visible in the sky during the day. An observer will note that the moon rotates about the sun once every day. The moon is actually slightly faster than a full rotation a day and will be at a certain positions in the sky at sunrise based on the time of year. An educated person can use this knowledge of where the moon is at sunrise in relation to north to determine a great deal of information. The position of the moon in the sky during sunrise will tell what month it is, the phase of the moon will roughly tell what day of the month it is, and the position of the moon relative to its sunrise will tell you what time of day it is.
For additional information about the stars and the constellations see the astronomy article.
Manifestation
Only unusual in that it behaves differently from our world. Otherwise it "looks normal."
Localization
This is visible anywhere in the world, provided you are able to see the sky.
The sun is stationary in the sky and the moon rotates about it.
During the day it's entirely possible to lose your sense of direction if you're not familiar with where the moon was during sunrise, though adventurers trained in survival shouldn't have this problem.
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Comments
Author's Notes
People will still want to own clocks as sometimes it is cloudy or they're indoors. Sundials are impossible in this setting.