Jaký je rozdíl mezi zemřel a umřel?
None, zemřít is slightly more formal.
Proč "nebylo" a ne "nebyla" ?
Because that is how we speak about age. "Je mi dvacet let." literally *"It is twenty years to me."
So matka (dat. matce) is an object, not subject. Subject is some implied "ono".
I had the same question... and now I just have a headache!!
Is the matce in locativ here?
It's actually in the dative! When you express ages like this in Czech, it uses the dative (even though 'matce' looks the same in dative and locative).