1) Can you damage the pirate boat without cannons?
Yes, but this takes a very long time. The Pirate Ship will have scuttled your ship and escaped before you can even do enough damage to board.
2) Do pets attack the pirate crew from your boat?
Yes, Pets are perfect to attack the Crew and then target the Pirate. You wont be able to damage the Pirate enough to kill him from your ship, but the pet will keep the Pirate occupied while you blow away his or her ship with your Cannons. Light Cannons are a waste. Just go for the Heavys.
3) Can one person without a crew manage to take down a pirate ship?
Yes and No You need to be coordinated enough to manuever your ship and fire cannons at the same time, while trying to keep your Toon alive. The Orcs can be taken down with 2 AIs from a good repond Bow, but your ship will take a pounding from the Pirate Ship's Cannons. Also depends on how many Cannons the Pirate has. If he has only one Cannon on each side it is easier.
I have taken down the Pirates using one Tamer and an Archer. The Archer steers the ship while the Tamer's Pet helps kill off the Crew and keeps the Pirate occupied.