Should we block any user action during the In App Purchase processing? 

What happens if the user presses back/ tries to cancel his transaction during the in app purchase processing?

Is there any callback/dialog appears in such cases from Roku?

Please see the docs on the ChannelStore node under DoOrder

If the user does not approve the order, the orderStatus field will be set to a ContentNode with fields reflecting the completion status of the command.

if you observe the OrderStatus field of your ChannelStore node, you should be able to see if the value changes.
 - Joel