Airtel - Receival of refund after cancellation of broadband

We had applied for an airtel broadband connection. Within minutes after registering online the technician gets in touch and arrives at our location to assess the fiber optic and wastes no time in taking the payment and necessary documents. This was on a Saturday night. We were assured that installation will be done on Monday morning.
Monday, we called several times, each time we were told that the connection will be done in * hours, * hours, end of day by *pm. The technician does not even pick up the call and even cuts our call.
At night, we decide on cancellation of broadband and apply for refund. Again after * calls to customer care we finally get the link to the refund page. On entering the transaction id, we get to know that our transaction has not even been listed! Airtel had been lying to us the whole day! When the transaction had not even been listed, how can they assure that connection will be given in * hours, * hours?
The next morning, when we called the customer care for the **th time, we get an sms that the connection will be done at ** Mbps, when we had paid for **Mbps. What kind of service is this!? There is no connection between the back end, customer care and the technician! No form of communication! We have applied for refund and the technician wants to come install it at a level, that is much lesser than that assured.
Now after calling for the **th time, they are telling us that our refund has been processed but what is the proof? Why can't I get an sms or an email stating the same?!