Can I use the Implied vol surface from the plain vanilla options to price the Knock out Barrier options with Rebate?. In addition, for risk management purpose, can I just imply the volatility from the Barrier option prices like in plain vanilla options (Black and Scholes Framework)
Implied vol as used in the market is purely a convention to express prices of vanilla options. The definition of implied vol is the number to plug into the Black-Scholes option pricing formula to get the right price for a vanilla option.
The fact that options at different strikes have different implied vols proves that the Black-Scholes dynamics (i.e. the assumption that spot follows a geometric Brownian motion) are incompatible with market pricing. If the Black-Scholes dynamics were correct, then the implied vol smiles would be constant.
Given that Black-Scholes market dynamics are incorrect, there is no reason they should give a correct price for any kind of path dependent option. Indeed market prices for barrier options do not match those that come from the Black-Scholes model.
One cannot even define an "implied vol" analogue for barrier options. This is because, unlike vanilla options, the Black-Scholes price of a barrier option is not necessarily monotonic in volatility. For low levels of volatility, the option price is near intrinsic value, but for high volatility there are counteracting effects of increased final payoff value but also increased probability of a barrier hit. The market price of the option may be higher than the highest possible Black-Scholes price. So there may be zero, one, or two levels of vol to correctly price the option.