Can any exercises that cause stress on the neck area trigger trigeminal neuralgia, or any positions that causes blood to rush to head?

Not believed so: TN is not believed to occur as the result of exercises placing stress on the neck nor positions which cause blood to "rush to the head." Some causes are DIRECT COMPRESSION of the nerve itself by a tumor, aneurysm, AVM, or blood vessel nicking the nerve. Surgeries, strokes, or MS can also cause damage to the myelin covering of the nerve causing pain. Need More info?www.healthtap.com/drsaghafi

Although a tortuous blood vessel intracranially might compress the trigeminal nerve, there is absolutely no vascular mechanism otherwise which would cause neuralgia, and not sure what you mean by blood "rushing to your head" unless you hang upside down. Neck exercises and postures may trigger pre-existing neuralgia attacks but do NOT cause it.