Is it a condition for a woman praying behind an Imam to see him, as is the case for a man, or is following him via loudspeaker sufficient, especially in areas designated for women's prayer which often obstruct the view?

It is not a condition for a woman praying behind an Imam to see him or some of the congregants. Rather, the conditions are the connection of the rows, that the women's prayer area be within the mosque's boundaries, and that the Imam's voice reaches her so she can follow him.

If the woman is unable to follow the Imam for any reason, she prays individually or prays with other women in a separate congregation if the Imam's voice cannot be heard or they cannot follow him. If she enters the mosque and hears the Imam's takbir (Allahu Akbar), she should not say it with him until she knows whether he is in prostration or bowing. It is safer to wait until the Imam says "Sami'a Allahu liman hamidah" (Allah hears those who praise Him) and then pray with him.

Ibn Abd al-Barr said: "And everyone who sees his Imam or hears him and knows his lowering and raising, and is behind him, it is permissible for him to follow him." Ibn Qudamah, regarding the ruling on a barrier that prevents seeing the Imam, said: "It is valid because one can follow the Imam without seeing him, like a blind person," and he stipulated hearing the Imam's voice.

In summary: If you are inside the mosque, hear the Imam's voice, and know what position he is in, then follow him. Otherwise, pray alone or with a group of women after the Imam finishes the prayer. As for the ruling on your prayer, Sheikh Muhammad ibn Salih al-Uthaymeen stated that it is safer for you to repeat the prayer.