What's the best way to tell that pasta is done (when boiling)?
Since al dente means "to the tooth", I always taste it and see :)

To my way of thinking, texture and cooked-ness are two different things. The heat cooks the flour which makes up the pasta, but the time in the water allows the water to be absorbed and soften it. A dry noodle soaked overnight in a cup of water might attain an edible texture, but wouldn't actually be cooked.

Taking pasta out of the water stops the texture from changing, except that too long sitting out and it can get dry again on the outside. Too long in the heat and it would overcook. Lucky that water boils at a pretty constant temperature (for your location/altitude), so once you get the timing right for a particular type of noodle, results are very repeatable.

I only remove pasta before it's done (par boil) when you're adding it to a casserole.