Hello,
as regards the URLs, it is no problem at all.
You can do it as you described and register new.mywebsite.com as Testing URL and mywebsite.com as Production URL. With the transition process as you described it, there will be no problems at all.
How long does it take since I pay and I can download the paid version? how is the procedure?
If you choose to pay online (with PayPal) then you get it almost immediately as the payment confirmation is automated. If you choose to pay by bank transfer it may take up to a few days before your payment is received on our account.
Have a nice day.