Brave weapon (or that Pegasus rider that can double ark with only a -2 speed) + desperation +brash assault seal

Nope. Desperation doesn't give more attacks, it just lets them come earlier, and brash assault doesn't stack with the double attack you get from just being fast enough.

No, 4 attacks is the maximum amount of attacks.
If you use a weapon that lets your unit double when initiating, and they outspeed the enemy unit with 5 speed, or the unit has a skill that lets the unit double you quadhit.

Give them an AOE special, and you can reach 5!. I mean...it'll be complete overkill, but go for it.

Galeforce.