Hello my mom an I are going to out of the country on the 13th of December her passaport is going to expires on April 7th does she need to renew her before she travels...thank you

I think it would be a good idea as they recommend at least 6 months before expiration for traveling out of country.

Would you be able to tell me how much it will be and how long it's take for her to get it if she goes tomorrow and play for it and thank you so much....

No

Specific passport validity requiments change depending on the country you are traveling too. Please visit travel.state.gov and look up where you are traveling too.