If it’s the US PS2 version, then yes, significant slowdown (on especially on the “arranged” stages with 3-D graphics) is normal. Which is why the Japanese version was always used for tournament play.
The Double Assault is one of the most overlooked but vitally important aspects of the gameplay.
It does only very light damage to normal life, but severe damage to red life which is recoverable.
This is important because characters recover life VERY quickly in this game after a period of time when tagged out.
HYPER CHARGE appears on the tagged out character’s lifebar once you connect with a D-Assault. What that means is that when that character is tagged back in, they are in a power-up state where their attacks do around +20% damage or so (which is BIG in this game). I remember hearing some people say that it also adds a little bit of frame advantage to your attacks and also makes the super meter charge slightly faster–can’t confirm it myself but I wouldn’t be surprised if it was actually true.
How long HYPER CHARGE lasts is variable. When the character is tagged in, generally going on the offensive and landing damage will make it last longer whereas being defensive and taking damage will end HYPER CHARGE mode much quicker.