Are transposing instruments always written higher than they sound?

Most of the time but not always the transposing descends but there are some exceptions. THIS link has a really comprehensive list of orchestral instruments and how they transpose. Piccolo - Sounds one octave higher than written.

1. What is a transposing sound?
2. What is the point of transposing instruments?
3. How do transposing instruments work?

What is a transposing sound?

In music, transposition refers to the process or operation of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant interval.

What is the point of transposing instruments?

Transposing musical instrument, instrument that produces a higher or lower pitch than indicated in music written for it. Examples include clarinets, the English horn, and saxophones. Musical notation written for transposing instruments shows the relative pitches, rather than the exact pitches, produced.

How do transposing instruments work?

A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). ... The instruments do not transpose the music; rather, their music is written at a transposed pitch.