This is because faceting in brilliant cuts maximizes the balance between life (brilliance) and fire (dispersion), faceting in emerald cut diamonds does not.
There is more flexibility in cutting of fancy shapes. Fancy cuts have recommended ratios of length to width.
The present market demand is higher for rounds (brilliants) than emerald cuts; but this can always depending on market conditions.
No, the number of facets can vary for heart shapes and pear shapes. Emeralds have the same number of facets.
The ideal proportion for a heart shape is 1:1 length to width ratio.