Is it possible to use Apple Pay to make payments at a terminal from an app?
Yes. See Apple Pay for Merchants - https://support.apple.com/en-us/HT204274
Is it possible to access the transactions made using apple pay?
If you mean view transaction details, no. Your app can only verify transactions.
Is it possible to access or retrieve payment information pushed to apple wallet?
Define 'payment information', but again purchase/payment info in your app is private to the user, and in the case of Wallet, the only 'info' there relates to passes, not purchases.