yes, this is not the way it is naturally pronounced. Nor is this a natural use of the word because why would anyone ever exclaim "because!!".
I think it has an awkward pronunciation because it is not in a natural sentence. It's almost always pronounced in two syllables (the e is silent)
F.W.I.W. Google translate sounds it out with the "e" pronounced. But they have the emphasis on the first syllable not the second as Duo did in this example. The effect from Google is that you can hear the "e" but not anywhere near as much. Much like you describe.
I'm curious. What region are you in?
Yes, it is fairly common. However, it closes conversation and can be taken as rude in conversation between equals. Adults might use it with children when they are too busy or exasperated to engage in prolonged reasoned explanations or requests. Supervisors might use it when they consider their time to valuable to be spent on explaining things to subordinates. Equals might use it in an ironic manner, to suggest that no one, least of all themselves, can explain why.