1d Wife that is most broad
W(ife) + ID EST (i.e. / that is) gives a word meaning most broad
14a Cultivating talent adds spice to keeping wild fern round Spain (5,7)
A talent for cultivating is GINGERS (adds spice to) around (keeping)an anagram (wild) of FERN itself around E (the IVR code for Spain)
15d Without a care, such infancy would be fashionable (5-4)
Without a care is the definition. Remove FANCY (fancy-free) from IN(FANCY) and the result is IN or fashionable