The definite article is often skipped in the superlative for äldst/yngst + dotter/son. I'm not really sure if there's an actual rule governing this. It's fine to use the den as well, though - I even prefer it generally.
The -e ending is historically used for grammatically masculine nouns. Nowadays it can be used in cases where it's clearly referring to a male, but -a ending is just as good to stick with (if not even better).