Hi Marco,
Responding to your specific question about the correspondence between Bishop Pierre d’Arcis of Troyes and the Pope’s response, at the end of the 14th century, you can find most of it, in its original Latin, on
archive.org, in a pamphlet published in 1900 by Ulysse Chevalier called “Étude Critique sur l’Origine du St Suaire de Lirey-Chambéry-Turin”. Translations are more difficult to come across, as they tend to have been copied from source to source, somewhat selectively. Typing “The case, Most Holy Father, stands thus” into Google will give you a variety of interpretations, and refutations, for that matter.
As to the Pope’s precise instructions about how the Shroud was permitted to be displayed, they are rarely translated, and what follows is my own.
"“As long as an ostentation lasts, no capes, surplices, albs, copes or any other kind of ecclesiastical garments or accoutrements are to be worn, nor any of the solemnities usual to the ostentation of relics performed. Torches, candles and tapers must be kept to a minimum, and no other kind of illumination used instead. And throughout the display of the said image, whenever a large crowd of people has gathered, it is to be formally announced to them, in a loud, clear voice, with no obfuscation, that the image or representation before them is not the true Shroud of our Lord Jesus Christ, but a painting or canvas made in the form of or as a representation of the said Shroud, of our Lord Jesus Christ.”
I hope this helps.