"Mi hermana mayor vive en México."
Translation:My older sister lives in Mexico.
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You are correct. Yes to both questions.
For future reference, if you have a similar question, it is a good idea to use a dictionary. Spanishdict.com is an excellent resource. Here is the entry for 'mayor', you can clearly see in the examples that the form does not change for masculine or feminine words. Plural form, however, is 'mayores'.