I Spanish, why is it "EL telegrama" and not "La telegrama"?

Because Spanish words of Greek origin that end in "ma" are all masculine. This also includes el problema, el dogma, el enigma, el programa, el tema, el drama etc.

La alarma and la mamá are not of Greek origin so therefore are feminine.

Many words in Spanish that end in "-ma" are of ancient Greek origin...this class of nouns was actually neuter in gender, and they remained neuter gender after being absorbed into Latin. In most Romance languages, these former Latin neuter nouns became lumped together in the masculine gender, hence "el tema", "el programa", "el problema", "el telegrama", etc.

El is always used for objects without a gender.

Nouns have gender. People and animals have sex. Objects do not have sex. This is important to know. Grammar may be boring, continuation of life and species depends on sex and reproduction.