Question

is the time period same for sun and moon
to appear at selected position after
Completing a cycle in the sky every day?​

Answer 1

So the Moon crosses the sky about 50 minutes later every day. And you might think it would rise 50 minutes later every day, and set 50 minutes later too. But this isn't true - because the Moon doesn't spend the same length of time above the horizon every day. The Sun goes through a seasonal variation, once a year.