Yes. 'Allegro vivace' is interpreted as a single indication, not two separate ones. Therefore 'assai' modifies 'allegro vivace', not 'vivace'.
No vivace is the fastest tempo (Faster than my internet)
The musical terms are defined as follows: 'allegro' -> fast 'assai' -> very 'vivace' -> lively
The root word "vivace" in music, derived from Italian, means lively or briskly. It is used to instruct musicians to perform a piece of music in a lively and spirited manner.
presto
yes
Vivace
amphetamines
I. Lento maestoso - Allegro molto II. Poco adagio - Vivace non troppo III. Andante - Vivace non troppo IV. Andante moderato V. Allegro VI. Lento maestoso - Vivace
Vivace
They are all tempos
It is an Italian word meaning 'lively'.