Questions...
Out of the noise of tired people working,
Harried with thoughts of war and lists of dead,
His beauty met me like a fresh wind blowing,
Cleaning boyish beauty and high-held head.

Eyes that told secrets, lips that would not tell them,
Fearless and shy the young unwearied eyes -
Men die by millions now, because God blunders,
Yet to have made this boy he must be wise.

1) What do the words/expressions "harried with", "high-held", "by millions" and "blunder" mean in the poem above?

- The following question is not concerned with the poem above; however, it is of similar importance:

2) Which of these words are considered to be more formal (to be used in a poem): "rapidly", "promptly", "quickly" or "fast"?

Question

Questions...
Out of the noise of tired people working,
Harried with thoughts of war and lists of dead,
His beauty met me like a fresh wind blowing,
Cleaning boyish beauty and high-held head.

Eyes that told secrets, lips that would not tell them,
Fearless and shy the young unwearied eyes -
Men die by millions now, because God blunders,
Yet to have made this boy he must be wise.

1) What do the words/expressions "harried with", "high-held", "by millions" and "blunder" mean in the poem above?

- The following question is not concerned with the poem above; however, it is of similar importance:

2) Which of these words are considered to be more formal (to be used in a poem): "rapidly", "promptly", "quickly" or "fast"?

Answer

Thank you very much, guys!

Answer

"harried with " - strained, stressed, distressed, bothered by ...(thoughts of war) 
"high-held" - in theory when we compound two adjectives or words serving as adjectives with a linked thought in front of a noun, we hyphenate them like this. It means he holds his head high, he stands up tall and straight. 
"by millions" - an ugly expression for "in millions", or, here, "millions of men are dying"
"blunders" - makes mistakes :( 
In English poetry, really, you can use any word at all, just using its sound, rhythm and meaning to contribute to whatever effect you are trying to achieve. I'd guess we could find all four of those words in good modern poetry. 
https://hellopoetry.com/words/fast/ 
https://hellopoetry.com/poem/2461932/pulse/ 
https://whitmanarchive.org/published/books/other/rhys.html 
https://www.poemhunter.com/poem/little-eyes/

Answer

1)
 'Harried' would mean like invaded by the thoughts.  
A high-held head means I head which is high (and not low) therefore implying a confident person.
'By millions' means in high numbers.
A 'blunder' is an error.
2)
 It depends on the context. Any of them would be good depending on how you use them within the sentence and how the sentence reads poetically.