Can I pay with my phone if I switch to Cyanogenmod? I own an Oneplus 3 and a NFC sim card. In order to use the banking payment app of my bank (Rabobank Wallet: https://www.rabowallet.nl/ / Netherlands) I need a phone with android supporting open mobile api as far as I understood. I read online that Oxygen OS does not have support for OMA, but Cm does. Will flashing CM make me able to pay with the Rabo Wallet app?

Bonus question:

Only very expensive providers support NFC payment in their sim card. Can I switch provider, (which has no NFC sim) place it's sim in slot #1 en the NFC sim (without data plan) in slot #2 and pay with the second one?
Yes flashing Cyanogenmod will enable you to pay using your banking app. Cyanogenmod does have support for the Open Mobile API.

 The Second approach however will be a bit tricky to do as I have not tried that. But I think its worth giving a try ! 
If it doesn't works, the first option will do just fine!.

PS : I like Cyanogenmod more than Oxygen OS, I suggest you that you use it as your daily driver.