Is the prayer of one suffering from obsessive-compulsive disorder considered valid if she is unable to recite the Fatihah completely due to the imam's speed, and she performs the glorifications and tashahhud quickly out of fear of the imam rising, thereby losing her devotion?

It is better for a woman to pray in her home, especially if that helps her achieve khushu' (devotional humility). Waswas (obsessive whispering) is an illness with causes and cures, and khushu' in prayer is a Sunnah (recommended practice), not an obligatory duty, according to the preponderant opinion. Therefore, your prayer is valid. In the future, you should pray in your home, as it is better for you. If you pray in the mosque, try to achieve khushu' to the best of your ability.