Hi Nathan, welcome to the community! 
As the prepaid card isn’t a credit solution so having / using it won’t affect your credit score.
Yes you can, you would need to contact the support team in order to do this, take a look at this topic for more discussion on this & a preview of the option to do this in the app.
From cancellation rights in the T’s & C’s -
If you change your mind about having the card, you can cancel it at any time without charge. We will refund any balance remaining on the card to you.
There is no contract / subscription / obligation to carry on using your Monzo card…but soon you’ll never want to use your old bank again 