Re: for to
"For-to" infinitives are well established in Chaucer, e.g.
At which the hooly blisful faire mayde
Gan for to laughe, and to the juge sayde...
Thou seyst thy princes han thee yeven myght
Bothe for to sleen and for to quyken a wight...
and occur in the King James version:
3. And this is the reason of the levy which king Solomon raised; for to build the house of the LORD...
By the end of the 18th century, though, they seem to have disappeared from standard English. I would say that (in BrE) they survive chiefly in dialect and folk balladry; or as a metrical expedient; or as deliberate archaism.
(I would guess that the Queen lyric represents a combination of expediency and archaism.)
Not a professional ESL teacher.