Yes!!! You got it!
Explanation is mostly very much on point. A couple lines were intended differently, but it doesn't change the answer.
Old friends are fallen on the road - "There’s that Ted Sandyman a-cutting down trees as he shouldn’t. They didn’t ought to be felled: it’s that avenue beyond the Mill that shades the road to Bywater." This whole stanza is still Sam seeing the marring of the Shire.
Stanza 4 generally speaks about Frodo's vision of things in the distant past or future, which he might not yet understand.
When battle breaks and prophecies of old will come to pass, - "prophecies" is the most loose line, referring vaguely to Aragorn's return as King hitting Paths of the Dead en route, which in combination sorta fulfills multiple legends. The first part is correctly identified to the exact quote.
When you are taking up the tale from heroes of the past, - "many swift scenes followed that Frodo in some way knew to be parts of a great history in which he had become involved". Specifically he sees the arrival of Elendil & co and the founding of Gondor, a story that must be completed by the Return of the King, the Battle for Gondor, and the destruction of the Ring.
When tempests rage and vessels sail to build, save, and depart - Then he saw against the Sun, sinking blood-red into a wrack of clouds, the black outline of a tall ship with torn sails riding up out of the West (ship coming to build Gondor); And then again a ship with black sails, but now it was morning again, and the water rippled with light, and a banner bearing the emblem of a white tree shone in the sun (ship coming to save Gondor; and into the mist a small ship passed away, twinkling with lights (ship departing Middle-earth).
And, like you have rightly concluded, the thing Sam sees at first and Frodo sees at the end of their visions, is the reflection of STARS in the Mirror.
The floor is yours! *bows out*