Intervals enharmony question

[Menu Jacques]

Hello folks,

Say I’m considering chords with an E flat root. 

Is is always true that:

        - the diminished fifth is B double flat
        - the augmented fifth is B natural

        - the diminished unisson is E double flat
        - the augmented unisson is E natural

or can this depend on the tonality of the music that contains these Eb based 
chords, say D major, in which case enharmonic notes should be used instead?

Thanks for you help!

JM