age
The German word for age is 'Alter'. It is used in the same way as in English, for example: 'How old are you?' in German is 'Wie alt bist du?'. 'Alter' can also be used to express age in years, as in 'Ich bin 30 Jahre alt', which means 'I am 30 years old'.
Dude, that was a cool party!
In this context, 'Alter' is used as a term of address among friends or equivalents, similar to 'dude' or 'mate' in English. The sentence states the speaker's astonishment about a past event.
I can't reveal my age.
Here, 'Alter' is used in its common meaning, which translates to 'age' in English. It reflects the speaker's unwillingness to disclose their age.
This is a monumental building from ancient times.
In this use, 'Altertum' is a variation of 'Alter', which implies a long time ago in a historical context, equivalent to 'ancient times' in English. The statement is discussing an old historical building.