Pushing Machine (Original) uses AdMob (https://www.google.com/admob/) to serve ads to the users. AdMob uses the device’s Advertising ID to serve personalized ads based on the users interests (which includes collecting and analyzing user data).
Pushing Machine (Original) uses Firebase (a Google product) which collects information about app usage. Example data usage collected: number of moves in the game, screen opened, very rough geographical location of the user (not more accurate than the name of the city and country). Data collected with Firebase is collected in such a way that it cannot be associated to a specific individual user or living person and therefore all data collected is completely anonymous. The only purpose for this data collection is for the developer to be able to understand the game usage patterns and make the game better thanks to this information.