A diminutive is “a word which has been modified to convey a slighter degree of its root meaning, to convey the smallness of the object or quality named, or to convey a sense of intimacy or endearment”: Diminutive . Well done there, Wikipedia.
So not so much an element of speech, but a modification of a word (typically a suffix), used to convey either that this is a smaller version of the thing, that the thing is cute, or that you like the thing/person.
So, a duck-ling is a small duck. A kitchen-ette is a small kitchen. A beast-ie is a cute beast. Annie-kins is Annie, who you like a lot.
When the cute/dear sense of the ending is dominant, you call it a hypocoristic . That is what is used by linguists to refer to English endings like –ie, which are much more about the cuteness than the smallness.
For the feminine sense, I refer you to Zhenrui Liao’s answer, for languages with grammatical gender. Languages without grammatical gender can still use a suffix just to refer to women. English could have gone that way (brun-ette, bachelor–ette), but hasn’t (kitchen-ette, leather-ette).
I can’t find it now, but someone on Quora has recently referred to the Australian English ending –ie as a feminine diminutive. Linguists call it a hypocoristic, because it’s much more about the cuteness than the smallness; and I’m not sure it’s even about the cuteness any more. (sickie for sick leave? mozzie for mosquito?)