México (and several locations inside Mexico) is one of the few Spanish words that aren't pronounced as they are written (it actually follows archaic spelling/pronunciation conventions).
The word should spelled "Méjico" according to current Spanish, but many people loathe that spelling, preferring to keep the archaic form.
Ser is for characteristics, place of origin, professions, permanent or semi-permanent traits etc. Estar is states of being that are usually transitory or temporary. ie. estoy enojado (I'm angry,) está casado (he/she is tried) están en la tienda (they are at the store.)
The "temporary" qualifier really is not the best way to remember when to use "estar." Instead, use the acronym PLACE as a mnemonic: Position, Location, Action, Condition, Emotion.
For example, we say "Está muerto" for "He is dead." Not something most people think about as temporary, but it does qualify as a condition.
By the way, "Está casado" is "He is married." You wanted to say "Está cansado," which is then "He (NOT she) is tired." ("She is tired" would be "Está cansada.")
In many cases, estar indicates a state but ser indicates that one CAUSES that state in others. For example, "Está aburrido," "He is bored," but "Es aburrido," "He is borING."