The second bank account is really more for protecting you against black swan events. If all your accounts are under the same bank and have the same owner, there's nothing stopping the bank taking funds from one of your accounts to make up for shortfalls in another.
The only reason I don't use them for everything is because I get better cashback/points with other cards.
I'm wary of giving my card information to companies outside India because I don't have this protection.
True for Indian companies but what if you get charged via Forex abroad? For me - Google or Steam - don't required 2FA. All I have to do is to enter my number, confirm CVV then zap. It gets debited. I do get a call from my bank (HDFC) asking if this transaction has been initiated by me, if I say yes, they let go.
The Flash UI looks like this http://mayoyo.tokyo/jJ7.png
They used to have a mobile app but it was discontinued since it didn't support 2FA.