Spectral Leakage, Phase and other questions about FFT
Windowing artifacts can be considered as due to a loss of information about a larger data set (e.g.what the window cut out or zeroed).  The "spread" of the Sync is related to the shortness of the data window (what's left after the information loss).  Thus other information about the original data from outside the FFT results can be used to help "solve" this problem (more data, perhaps used with longer FFTs, results in a narrower Sync main "hump").

Phase information within each FFT aperture plus the distance between adjacent or overlapped frames of FFT data is used in to refine phase vocoder frequency estimates or to aid in signal reconstruction.  Phase differences between frames taken from differently placed microphones can be used to help triangulate sound source location.

Peak amplitude can be estimated by interpolation equations, such as parabolic interpolation from 3 points, or better, from (windowed) Sinc kernel interpolation with successive approximation to find the zero derivative point.