This is true.
Not quite. The Milky Way is about 100,000 light years across, so the light at the very most would be 100,000 years old, although it's not that old because the Earth isn't at the very edge of the galaxy. The light coming from a star is only as old as the star is distant in light years. If you're including the time it can take for a photon to escape the core of a star (somehow I don't think you are), that age could be inflated by
up to a couple million years, depending on the size of the star.
You know the biggest known star Betelgeuse?
No, the largest known star is NML Cygni. It's almost twice the size of Betelgeuse.