"Why did the armies and men of Epirus switch to Parmenion?"

We were told the King had gone mad with a sickness of the mind and then that he had died. Parmenion is a powerful man, one of the few who managed to survive from the days of Macedonian control, before Alexander came to power. It seemed natural to follow him. You must remember that Alexander was brought to power through a civil war, aided by Rome. As before the war there are people that did not support his ascension to power, hence why there is support for Parmenion now despite Alexander begin alive.

"Where do they receive their supplies and reserves from? It seems to be, from my intelligence, south of Stratus..perhaps towards Macynia or another port due to the ships at Ambracicus Sinus."

The south of the country and Macedonia, well that was until they seemingly broke off supplies some months ago. Plus he pretty much gutted Dodona when he left, I am sure.

"If we hold a seige here, which I will be recommending....can we setup our castra on the high hills southeast of Ambracia...where we would be well out of range of their weapons, yet they would be vulnerable to ours?"

The catapults would almost certainly be out of range, perhaps the balistae might reach, but they would lack any real punch. The only way to find out is to try it. Personally I doubt it will work.

"Since Arachthus F. flows through Ambracia..surely there must be hidden means of getting into the city. Is there?"

There are bound to be outlet and inlet pipes, but they will no doubt be defended and barred. We can of course try.