What are you talking about.
... could well ask you the same question, since you're mixing your FE and RE theory below, and can't seem to make up your mind which one you want to cite.
For 14 days the moon will be on the same side as the Sun.
Yes, that would be, in RE, the hemisphere that faces the Sun. Which changes (for those on the surface) with every Earth day and night as the Earth rotates, so you move through that hemisphere.
Day will alway be on the same side as the sun and nights will always be on the opposite side of the sun. FE rotates every 24 hours so everyone on a RE has a night and day and every night is on the same side. Which is the opposite that the sun is on.
Yes. And those days and nights, for those on the surface, move under the Moon on RE, which only moves (24/360 = ) 7 degrees of its orbit for each Earth night and day, with the observers moving 360 degrees in the same time.
Take a quarter and run it from one side of the sky to the other and see how many stars you pass over. Thats how many stars the moon should pass over on the 14 nights the moon is on the opposite side of the sun. The other 14 days it’s on the same side as the Sun, shouldn’t even be seen at night. But yet it is.
What does that tell you, since you think it "shouldn't be seen"? All the observational evidence of every human, ever, contradicts what you think should happen, but tallies exactly with the textbooks (which were written by a group of the millions of astronomers who have studied it as their life's work), the experience of everyone who has studied the Moon, travelled to it, or sent craft to it. It only took me half a minute to find the two videos above which show exactly the event that you claim is not happening ...
Is Astronomy your life's work? How long do you spend looking at the Moon, in comparision to professional astronomers?