If you mean the vertical poles to which sails are attached, these are called masts.
If you mean the vertical poles to which sails are attached, these are called masts.
The ship or boat with sails is the yawl, which will typically have 2 sails, the main mast for the main sail and mizzen mast. A yawl is defined as a boat with the mizzen mast aft of the rudder post. A boat with two masts, a main mast and a mizzen mast with the mizzen mast forward of the rudder post is a ketch.
Its rigging
A rowboat?
Unfurled and rigged means that they have "rigged" the boat, meaning put the masts up, and set the boat up so it is reads to go, and unfurled meaning unrolling the sails.
There is a boat called a dory, though they seldom have sails
the masts
I believe it is called a "spar".
masts
A brig
Fx Sails offers quality and affordable sail boat sails. You can find them at: www.fxsails.com/. In your town, there should be marinas near where you launch your boat that will offer sail repair.