In reality, it depends on whether your broker has, or can get, the shares to loan you for the short sale. Generally speaking, ETF's that trade heavy volume (i.e. SPY, QQQ) are shortable. However, thinly traded ETF's are typically NOT shortable.
Yes, depending on how many shares of the ETF trade on average and the rules of your broker/dealer. There are also some "Inverse ETFs" that will short the asset for you that you can buy long and not need a Margin Agreement and with potentially less cost. Also, there are "Leveraged Inverse ETFs" if you are particularly convinced of the strategy. Once again, there are risks and some firm will not allow the specialty ETFs to be traded or may require you sellout the same day. Good luck.
Generally speaking, yes you can.
You can short an ETF, but its not as easy as purchasing an inverse fund that will do the same thing for you. In addition, you can hold an inverse ETF in an IRA or other tax qualified account that does not have margin enabled. The biggest providers of inverse ETFs are ProShares and Direxion funds. I prefer ProShares because they have single beta short funds that don't employ leverage. In my opinion leverage is one of the most dangerous things for most retail investors because of the magnification effect of losses and the problems with compounding over time. I would only us an inverse strategy with a very small portion of your portfolio. Best of luck.
ETFs can be sold short. However, the illiquid nature of certain ETFs (and some thinly traded stocks) can make shorting them very expensive. Large, liquid ETFs are the best candidates to short if you have a strong view.