I don't think either of these work, because a spell is a card or copy of a card on the stack. The triggered ability, in the case of Samite Ministration, can't come from a spell because Samite Ministration has left the stack at that point. The same for Chant of Vitu-Ghazi, though it's not a triggered ability in that case.
The wording "causes you to gain life" on Firesong and Sunspeaker, which is a complete novelty, is the cause (no pun intended) of a lot of debate among rules experts currently. Until a new version of the Comprehensive rules is released with Dominaria, it is difficult to answer questions such as these with certainty. Even asking WotC's MTG Rules Manager Eli Shiffrin about this, if he answers, is no 100% guarantee of having a definitive answer of how these interactions will work when the set is released, because he and his team may still have to patch some holes and find some solutions to unforeseen interactions at the moment. My answer is that we will have to wait and see.
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I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
The life gain from Samite Ministration is due to a triggered ability (C.R. 615.13), not from a spell, so it won't make Firesong and Sunspeaker's last ability trigger. See also this thread.
In the case of Chant of Vitu-Ghazi, the damage prevention effect happens at the same time creatures would deal damage (C.R. 615.5), so even while a white instant or sorcery spell is resolving (e.g., Repentance). It remains to be clarified whether the phrase "a white instant or sorcery spell causes you to gain life" means "you gain life during the resolution of a white instant or sorcery spell" (compare Firesong and Sunspeaker with Karmic Justice or Equinox).
One ruling for Firesong and Sunspeaker, now found in Gatherer, reads, in part: "A spell causes you to gain life if [among other things] an instruction in its cost or effect is modified by a replacement effect and the modified event includes you gaining life." Although the ruling speaks of replacement effects, note that C.R. 615.6 says the following about damage prevention (as in Chant of Vitu-Ghazi): "If damage that would be dealt is prevented, it never happens. A modified event may occur instead...."
Thus, if Chant of Vitu-Ghazi prevents damage Repentance would deal and makes a player gain life equal to the prevented damage (see also C.R. 615.5), then that would normally count as a "white instant or sorcery spell" (here, Repentance) "caus[ing] [a player] to gain life".
I don't think either of these work, because a spell is a card or copy of a card on the stack. The triggered ability, in the case of Samite Ministration, can't come from a spell because Samite Ministration has left the stack at that point. The same for Chant of Vitu-Ghazi, though it's not a triggered ability in that case.
If Chant of Vitu-Ghazi does combo with Firesong and Sunspeaker, does that mean Hallow can as well, assuming you cast it on Firesong and Sunspeaker while they're on the stack and then trigger their ability after they resolve?
In the case of Chant of Vitu-Ghazi, the damage prevention effect happens at the same time creatures would deal damage (C.R. 615.5), so even while a white instant or sorcery spell is resolving (e.g., Repentance).
It remains to be clarified whether the phrase "a white instant or sorcery spell causes you to gain life" means "you gain life during the resolution of a white instant or sorcery spell" (compare Firesong and Sunspeaker with Karmic Justice or Equinox).EDIT (Apr. 18): See comment 4.
Thus, if Chant of Vitu-Ghazi prevents damage Repentance would deal and makes a player gain life equal to the prevented damage (see also C.R. 615.5), then that would normally count as a "white instant or sorcery spell" (here, Repentance) "caus[ing] [a player] to gain life".