That actually makes a lot of sense as a woman is going to be most fertile when she ovulates, shortly after her period is over.
I would expect that to be the most likely.
What makes David's betrayal of Uriah worse was that Uriah was one of David's closest, trusted warriors.
He is listed in 1 Chronicles 11 and 2 Samuel 23 with many other of David's mighty men, and the reading of the passages implies that Uriah was one of David's body guards.
Yes.
It seems most likely Uriah knew what was going on.
The Court and City of Jerusalem was not that large.
Uriah had friends in the King's guard.
They had wives.
The wives talked, the servants talked.
You cannot keep that sort of secret in that sort of setting.
There was no sort of "privacy" such as exists in large urban centers of today.