Will it affect you in any way if Binance completely shuts down ?
Not anymore. Since my Binance Visa debit card is expiring in a few months and Binance didn't find another card partner I withdraw everything i had there (which was not much btw) so no, I personally won't be affected much.
I know there will be lot of devastating affects on crypto market of this incidence like bitcoin price will fall very sharply.
Drop will be significant indeed, but only in the short-middle term. Bitcoin price would eventually recover and everything would be back to normal, like it happened in the past.
Many users will also loose funds and some will loose faith on crypto.
Some will maybe losse fait in crypto, but you would have to be very ignorant to loose "faith" in bitcoin just because you trusted some centralzied entity to store your money, going directly against everything bitcoin stands for.