Making a promise/vow without saying it verbally

Q:

1. If a person promises something to Allah without verbally uttering it, is the promise binding? If he/she does not fulfill the promise will he/she be sinning?

2. If someone says to Allah that I will do such and such, but he/she did not say the word ‘promise’ to Allah and nor did he/she use the word ‘vow’ or ‘oath’. In this case, if the person does not do such and such action, will he/she be sinning?

Mistakenly receiving extra money into one's account

Q: I'm using a banking app, so I have transferred funds from 1 account to another but the transaction failed and the balance has been deducted from my account. After a few minutes, I received a refund but my 2nd account has also been credited with that amount... So I'm asking that should I return it to the merchant as I have been paid this extra amount mistakenly.