Shudder when idling and a hesitation when accelerating

Hi I have owned this car for a week, its a automatic but has the option of putting it into manual or flappy padels.
never owned a auto so 2 questions maybe normal or not
since we collected the car we noticed when sitting at lights idling it shudders not a huge amount but its noticeable and now the last 2 days its hesitated when pulling away from idling.
So firstly is it normal for a auto to shudder while idling?
Secondly any ideas what maybe causing the hesitation this is definitely a new thing as it wasn't doing it the first 4 days.
With the hesitation its only while pulling away not when your in for example third to fourth, and the hesitation is in any mode full auto for manual mode,
thanks in advance for any advice.
Ps the garage gave a 3 month warranty with the car but im asking for advice first as I don't want to sound like a idiot due to my first auto.