EV/FCF

If you had to, you should use unlevered FCF. However, EV/EBITDA is preferred to EV/FCF because EBITDA is theoretically more difficult to manipulate and less volatile (disregards taxes and capex which vary from year to year). With that said, there's always debates on whether or not to include tax/capex in multiples calculations, especially if these are expected to be relatively constant on an annual basis.

yes; for the second questions, (EV/FCF)*FCF=EV mathematically, so you obviously can, but this is usually a bit of a lumpy multiple...

When you're using multiples, you have to make sure the numerator and denominator match - the earnings/CF/etc in the denominator must be those attributable to the claimholders included in calculating the numerator. EV/EBITDA is logical because the numerator includes the value of both equity and debt claims while the denominator is earnings which are attributable to both equity and debt holders. Another example - if you're looking at a business with a minority owner, and EBITDA does not already subtract out earnings attributable to that owner, then in calculating EV for the EV/EBITDA multiple you must add the value of minority interest. If you always remember that the numerator/denominator must match in this way, then it becomes obvious which multiples make sense (EV/unlev FCF makes sense, EV/EFCF does not).

EV/FCF is an important metric in one sense because free cash flow generation is ultimately what you care about as the owner of a business. You can't spend EBITDA or EBIT, you can only extract from the business the FCF it generates. As the others have mentioned, however, FCF is often too lumpy to really compare businesses based on EV/FCF multiples. EV/EBITDA and other multiples are used because they are less lumpy / behave more nicely, but you have to keep in mind that such multiples are only useful if you are comparing two businesses which, in the long run at least, can translate EBITDA to FCF at the same rate - i.e., in the long run they will have similiar capex needs, working capital needs, and tax rates. That is true for very few pairs of companies, which is why EV/EBITDA is generally a terrible metric.