Yes, didgeridoo. A study that appeared in the british medical journal in 2006 showed that regular playing the didgeridoo (the australian aboriginal instrument) was helpful for obstructive sleep apnea. One potential reason is that to play the instrument one must learn "circular breathing" and thus not obstruct the airway. But you don't have to necessarily learn to play it, just learn the breathing technique.
Yes. Opening the nasal and/or pharyngeal airways may help. The adhesive strips applied to the outside of the nose (breathe right) can help open the nasal airway as can some natural sprays (saline and others) used in the nostrils. Removable oral appliances can help open the pharynx at the back of the throat.