How does the price system works?

Hello everybody. I've started uploading my very first course but I do not understand how the pricing system works: is it possible to me to change the price of the course after it has been published? I'd like to offer it for 9,99 until I receive some reviews (I hope good reviews) and then increase the price.

Second question, how does the discount system of Udemy works? If I remember well, I accepted that Udemy changes the price temporarily for a better selling, but I'd like to understand more.

Thank you for your support