Green is recharged here but how?
Pay close attention to the life gauge at the moment he gains green on his meter. It bounces, indicating he got hit by a red laser beam. Every time a laser beam touches you, you take slight damage (1/20th I think?), but you also recharge Phantom meter, so if you get hit by a laser you can immediately transform after the first hit to protect yourself (or in this case use it for score). The sound effect/yelp of pain you normally hear can't be heard, but that's probably because of all the other sounds caused by the katanas hitting the enemy.
Do i need a specific shot type to continue the hit counter?
Outside of your transformation mode (as in when you're a plane) the hit counter is maintained by using the rapid shot (Akai Katata refers to it as the defense shot) so use that when you want to attack and keep your hit chain. You basically need to use the rapid shot every so often in addition to the stronger held shot to keep your chain in Slash Mode if I'm not mistaken. The rapid shot will visibly build hit chain, whereas the hold/laser/attack shot (whatever you want to call it, the one that's thinner/stronger) won't. When you're transformed, I think your hit counter is maintained without shooting at anything so you can transform and focus on timing your katana launch without losing your chain.
It's been a while since I've played Slash seriously though so I could be mistaken.
A recharge with blank meter.. how does this happen?
Same thing as in stage 1 - they let themselves get hit by the red laser (you can hear the pain sound effect) in order to get the meter recharge.
Asure wrote: guess if they made a Matsuri version slash would have been it.
They actually made a couple special versions, White & Red. No console ports yet.
http://www.youtube.com/watch?v=JSfM9g4DWxs
http://www.youtube.com/watch?v=p6AYmJaIzIg