Not necessarily. Presumably you, as the app developer, are operating your own servers with players' account information so that you can unlock their purchases after they pay. Your server should be running its own wallet, and it can check its own wallet to see if a payment has confirmed.
Still few questions:
1. Where my app can get Transaction ID to check its status? (I suppose only manual enter by user).
You should be checking it on your own servers and informing the app that the payment has confirmed. Your own servers should be handing out a new address for every single purchase so that it is easier to track people's payments to you. All you need to do is watch for transactions for each address, and then notify the app when those transactions confirm.
2. I am not sure that there is programming interface in this wallet to interact with another apps. My goal is to get payment confirmation programatically.
Again, your servers check this, and then relay the information to the app. The app should not be looking for this information itself.