1. I don't know much of smile trading. If it is a skew, then buy puts. Since when stock price goes down, the volatility will go up much.

2. put has gamma+ and Vega+ and is positively affected by dividend. ,stock has 0 gamma, 0 vega and the current price has nothing to do with the dividend.

3. call and put's gamma can be seen as symmetric and gamma itself is symmetric at the ATM point. The shorter the time to maturity, the higher the gamma. So 3 month call has a higher gamma than 6 month put.  The same is Vega, the option with longer term is more sensitive to the change in volatility. Only the dividend expected within the option's life has effect on the option price.

4. If the market is calm, which means no much change in volatility, there is no need to buy the option(buy option is roughly equivalent to long the volatility) So sell it and earn the premium and the same time delta hedge the risk of the change in underlying price.

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1、Smile, sometimes called "skew",  represents how different options’ volatilities relate to each other in any given contract. If the skew is flat, it means the options are oversold,and traders always buy OTM puts. So I think the answer is C.