Will medications that treat anxiety help my sleep apnea?

None. There are no fda approved medicines for the treatment of sleep apnea. If you have apnea, the first line treatment is cpap. It is a serious medical problem that should be treated...
No. In fact, if it is a benzodiazepine medication it can actually make it worse. Also, if it is a medication that causes weight gain it can worsen it. Ssri medications can also fragment your sleep, but will not worsen your apnea per se. Alcohol definitely worsens sleep apnea.
No. Depends on the class. Benzodiazepines (e.g., lorazepam, clonazepam) relax the upper airway and can make obstructive sleep apnea worse. Previously, studies were done to see if ssris might be helpful in osa by decreasing rem sleep. However, these were not conclusive and we do not use these specifically to treat osa.