Add to list for The Land where the Shamrocks grow (Star of the County Down):
Van Diemen's Land ( Come All Ye Gallant Poachers)

For The Red-haired Boy, add Matt McGinn's Lots of Little Soldiers.
And he has two songs to the tune of My Bonnie Lies Over the Ocean, namely Skin, and Right Proper Bar Steward.

Hey Tuttie Tatie is used for 3 of songs, 2 of which are by Burns: the song by that title appears in The Merry Muses cantata, then there's Scots Wha Hae. And to the same tune, but much slower and more lyrically, Lady Nairne's song "Land O the Leal" (a friend said he'd been singing it for years before he realised it WAS the same tune as SWH!)

More Burns:
Dainty Davie, There was a lad born in Kyle (Rantin Rovin Robin), and The Gairdener Wi His Paidle (When Rosy May) all to the same tune.

As for how tunes become song melodies, Green Grow the Rashes was originally a very snappy strathspey, as is Miss Admiral Gordon's Strathspey which has been slowed down and smoothed out to provide the tune for "O A the Airts": the first half of the tune is also used for The Scarborough Settler's Lament in the smooth lyrical version.