Forgive me if my questions are too obvious but I'm new at this too and can tell you what I did to set this up. Are you logged into your Google Playstore account when you tap those purchase links? I set my preferences for allowing or disallowing purchases on my mobile devices from my PC at the Google Playstore site on my 'account' page under 'preferences.' I chose the device, that was already showing there because I'd downloaded apps off that site onto my devices, allowed purchases but requiring a new login - just in case somebody else used my device.
Did you get your apps from the Google Playstore or elsewhere? If you got them from Google Playstore, that is your payment gateway and all business you do with the app developers goes through it - that is for your protection. You register what credit card number you want to use on your Google account page, so you don't have to spread it around a lot of different directions.
The other obvious thing to check is your connection. I live out in the country so I'm accustomed to this issue. I may have plenty for browsing about but not enough to load and keep the Playstore, a graphic-laden and slow-moving site. It'll 'time out' and tell me to try again, and will behave if I keep trying. Even on my PC, I often have to refresh a page a couple of times so it will respond when I click on an 'install' button. You may be tapping inside your app of choice, but you're still trying to load that Playstore gateway in order to buy something so it's best to make sure you're not also using your connection for other jobs at the same time.
P.S. There is also Amazon! I forgot to mention that. Your gateway is your Amazon account and on any new Android device you may have, Amazon is likely already installed, for you to be able to buy apps there conveniently. You will have a card number registered there - or you can change it to another when you feel like it - and it works the same as Google.