From: Rabbi Moshe Sofer
To: Rabbi Yisrael
On the first question, the Chasam Sofer distinguishes the bride's status as muchzak from mere tafisah but notes her claim runs counter to prevailing custom, and recommends compromise. On the second question, he rules the wife should immerse on time so marital relations remain immediately available, but expresses reservations about the arrangement's propriety given concerns of coerced consent and the ongoing obligation of procreation.
Source: Shu"t Chasam Sofer EH I §129