What are the characteristics of a "good" smoothing convolution kernel?
Yes, in general, your #2 is correct.  That being said, both of the filters stink (with your triangle filter being a little better).

No, f3 does not have the same frequency response as f4.  To get an idea of why that is so, you generally have to zero-pad the impulse response before DFT'ing it to get a reasonable idea of what its frequency response looks like.