Hmm....do you use detailer spray with wet wipe? You're using good water but check around your home if there are white salts/deposits around taps, faucets, sink etc.
I'm thinking the straight line swirls on the hood imitate how you use the wash mitt......if no one else cleans it then we know that the swirls coming are your fault :P, serious. Again, i'm emphasizing on using the manufacturer's advice on the back of car wash or any other product.
Direction doesn't matter; up, down, right, left, zigzag......any direction used will cause swirls. Think about it; if there's dirt on your car and your cleaning/washing it in circular motion then it can be swirled up but if you're doing it up and down your car miraculously becomes swirl proof :P......thats not the case; swirls are not round......they are millions of tiny scratches that go in all directions. Look at your car in shade after wash; you'll see straight line scratches but if seen under a source of light they APPEAR circular but infact they were going in other directions.
Do take pics of the black lines. Do they fade away or become less prominent after some time? Or they stay as they are until you use liquid polish? Don't give too much drying time or the wax can cake on the paint and get hard to remove; if instructions say to wax panel by panel or anything else then stick to that.
While waxing look parallel to the panel to see wax application; you only need a thin layer and if you see wax is missing out then apply a little wax to applicator and keep waxing. A dry, clean pad will fill up with most of the wax before it really gets applied so spray some water on pad before putting wax on pad. This will ensure an even layer and you'll get less or no leftover wax on applicator. Try it in next session.