Compare Shu Yun, Possibility Storm, and Guttersnipe with Eye of the Storm. The first three have abilities trigger whenever certain "spell(s)" are "cast", even if they are copies of cards (C.R. 112.1b, 706.12; for prowess, see C.R. 702.107a). Eye of the Storm's ability, on the other hand, triggers "[w]henever a player casts an instant or sorcery card", so not if a player casts a copy of a card due to Eye of the Storm (while a copy of a spell or of a card that's cast is itself a spell [C.R. 706.10, 112.1b, 706.12], a copy of a card is not a card for the purposes of Eye of the Storm [review C.R. 109.1]).
EDIT (Jan. 5): Some rules were renumbered with Core Set 2020.
Bored at work and came across this thread and now am quite curious as to some of these interactions. Can someone verify if I have this hypothetical situation right in my head?
Assuming you have cast Divination from your hand and Divination is a card:
Yes. Also, all the spells involved in this scenario are instant or sorcery spells and not creature spells, so both abilities of Shu Yun and Guttersnipe's ability will each trigger seven times in this scenario (C.R. 112.1, 112.1b, 706.12; for prowess, see C.R. 702.107a).
EDIT (Jan. 5): Edited, including because some rules were renumbered with Core Set 2020.
I̟̥͍̠ͅn̩͉̣͍̬͚ͅ ̬̬͖t̯̹̞̺͖͓̯̤h̘͍̬e͙̯͈̖̼̮ ̭̬f̺̲̲̪i͙͉̟̩̰r̪̝͚͈̝̥͍̝̲s̼̻͇̘̳͔ͅt̲̺̳̗̜̪̙ ̳̺̥̻͚̗ͅm̜̜̟̰͈͓͎͇o̝̖̮̝͇m̯̻̞̼̫̗͓̤e̩̯̬̮̩n͎̱̪̲̹͖t͇̖s̰̮ͅ,̤̲͙̻̭̻̯̹̰ ̖t̫̙̺̯͖͚̯ͅh͙̯̦̳̗̰̟e͖̪͉̼̯ ̪͕g̞̣͔a̗̦t̬̬͓͙̫̖̭̻e̩̻̯ ̜̖̦̖̤̭͙̬t̞̹̥̪͎͉ͅo͕͚͍͇̲͇͓̺ ̭̬͙͈̣̻t͈͍͙͓̫̖͙̩h̪̬̖̙e̗͈ ̗̬̟̞̺̤͉̯ͅa̦̯͚̙̜̮f͉͙̲̣̞̼t̪̤̞̣͚e̲͉̳̥r͇̪̙͚͓l̥̞̞͎̹̯̹ͅi͓̬f̮̥̬̞͈ͅe͎ ̟̩̤̳̠̯̩̯o̮̘̲p̟͚̣̞͉͓e͍̩̣n͔̼͕͚̜e̬̱d̼̘͎̖̹͍̮̠,͖̺̭̱̮ ̣̲͖̬̪̭̥a̪͚n̟̲̝̤̤̞̗d̘̱̗͇̮͕̳͕͔ ͖̞͉͎t̹̙͎h̰̱͉̗e̪̞̱̝̹̩ͅ ̠̱̩̭̦p̯̙e͓o̳͚̰̯̺̱̰͔̘p̬͎̱̣̼̩͇l̗̟̖͚̠e̱͉͔̱̦̬̟̙ ̖͚̪͔̼̦w̺̖̤̱e͖̗̻̦͓̖̘̜r̭̥e͔̹̫̱͕̦̰͕ ̗͔̠p̠̗͍͍̱̳̠r̰͔͎̰o͉̥͓̰͚̥s̟͚̹̱͔̣t͉̙̳̖͖̪̮r̥̘̥͙̹a͉̟̫̟̳̠̟̭t͈̜̰͈͎e̞̣̭̲̬ ͚̗̯̟͙i͍͖̰̘̦͖͉ṇ̮̻̯̦̲̩͍ ̦̮͚̫̤t͉͖̫͕ͅͅh͙̮̻̘̣̮̼e͕̺ ͙l͕̠͎̰̥i̲͓͉̲g̫̳̟͈͇̖h̠̦̖t͓̯͎̗ ̳̪̘̟̙̩̦o̫̲f̙͔̰̙̠ ̹̪̗͇̯t͖̼̼͉͖̬h̹͇̩e͚̖̺̤͉̹͕̪ ͚͓̭̝̺G͎̗̯̩o̫̯̮̟̮̳̘d̜̲͙̠-̩̳̯̲̗̜P̹̘̥͉̝h͍͈̗̖̝ͅa͍̗̮̼̗r̜̖͇̙̺a̭̺͔̞̳͈o̪̣͓̯̬͙̯̰̗h̖̦͈̥̯͔.͇̣̙̝
EDIT (Jan. 5): Some rules were renumbered with Core Set 2020.
Eye of the Storm and Possibility Storm are both on the battlefield. Lightning Bolt is in exile from Eye of the Storm. I cast Divination and stack the triggers so Eye of the Storm is on top. I then exile Divination and cast copies of Lightning Bolt and Divination and after the copies resolve, Possibility Storm's trigger now resolves revealing Lava Axe (I choose to cast) which then triggers Eye of the Storm because it is a card. I now exile Lava Axe and cast copies of Lightning Bolt, Divination, and Lava Axe. Is this right?
Also, in this scenario, Shu Yun, The Silent Tempest and Guttersnipe would each trigger seven times, yes?
Yes. Also, all the spells involved in this scenario are instant or sorcery spells and not creature spells, so both abilities of Shu Yun and Guttersnipe's ability will each trigger seven times in this scenario (C.R. 112.1, 112.1b, 706.12; for prowess, see C.R. 702.107a).
EDIT (Jan. 5): Edited, including because some rules were renumbered with Core Set 2020.