Are there any specific words in English for male cousin and female cousin?
No, not single words. ] ).
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No, not single words. English is not as rich in relationship names as some languages (possibly because family relationships, while of course still important, are not quite so important in English-speaking cultures as in some others[original research?]).
When referred to with respect to your mom or dad, or aunt or uncle, there are:
"She's my mom's niece." (That is, she's my female cousin.)
"He's my mom's nephew." (That is, he's my male cousin.)
"I'm her nephew." (If "her" is your aunt, then this identifies you as a male cousin to any children she might have.)
"I'm his niece." (If "he" is your uncle, then this i