Two Russian Questions
Can I say "Мне" even though I'm female? Or is it okay for both genders to say (or that men mostly would use it)? Or should I just say "Мня"?

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And how should I say "This is my house" as a female?

Thanks in advance.

Question

Two Russian Questions
Can I say "Мне" even though I'm female? Or is it okay for both genders to say (or that men mostly would use it)? Or should I just say "Мня"?

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And how should I say "This is my house" as a female?

Thanks in advance.

Answer

"Мне" is a dative case of "Я" ("I" or "Me") and means "To me". It's used independently from the gender of speaker. For example: Он дал это МНЕ - He gave it TO ME.

You can say "This is MY house" as "Это МОЙ дом". 
"Мой" is a possesive adjective and stands for "My", which is changed due to the gender of the object, it is applied to. For example: МОЙ дом (MY house - masculine), МОЯ жизнь (MY life - feminine), МОЁ мнение (MY opinion - neutral), etc.

Answer

you would say 
это мой дом
it doesn't matter if you're boy or a girl, as house -  дом is masculine.

Whether you use мне or меня depends on the case, what you are trying to say

http://ru.wiktionary.org/wiki/%D1%8F

Answer

For both genders right to say "Мне".
No such word "Мня"

This is my house - "Это мой дом" (for both genders)

http://ru.wikipedia.org/wiki/%D0%9B%D0%B8%D1%87%D0%BD%D1%8B%D0%B5_%D0%BC%D0%B5%D1%81%D1%82%D0%BE%D0%B8%D0%BC%D0%B5%D0%BD%D0%B8%D1%8F