How does Channel (the Kamigawa mechanic, not the card) work when your commander has such an ability, such as Arashi, the Sky Asunder? Can I use it from the command zone? Do I pay the tax when I use channel? Does it increase when I use channel?
You cannot use channel from the command zone. Channel is an ability that has both a mana cost, and the requirement to discard the card. Discarding a card is only from your hand, not from the command zone.
This means you need to somehow get your commander into your hand (such as with Command Beacon or Road of Return). Once they're there you can activate their Channel ability and discard them, and this wouldn't involve the commander tax since it doesn't involve casting your commander from the command zone.