Now from 11:30PM my DSL and internet has started to off again. RSS errors are showing as you can see on the screenshot attached.
I assume your ADSL filter is in place and the connections have been plugged in correctly to both outputs i.e. one to the telephone and one to the modem.
Other than that, the carrier drop is a classic sign of noise on the line. I used to face this issue on and off with my BSNL connection back in the days. Pick up the telephone receiver and hear for static or other noise. If it is inaudible press any # on the dial pad so the dial tone goes off (it assumes you are dialling a telephone #) and listen for hum/static.
Generally during the monsoons water seeps into the cables and causes problems. If this doesn't resolve itself soon you need to contact BSNL and have them do a line test and switch the line pair that connects to your place. Only BSNL can resolve this.