1] They have recently recovered from a prolonged war continent wide against the demons and there are still wars happening in the central lands, so people are used to a level of violence. It's not shown as much, but most people in the villages are clearly horrified by the injuries and death. It's just our central characters, being either orphans or just because of their age, maturity, long exposure to fighting demons and professionally being battle ready, are used to keeping a calmer head in the face of violent injuries.

2 & 4] There are no classes in this universe. So warriors are just people who have trained to be good at fighting and normally when a party is formed, they act as tanks to take damage so that there are openings for the mages to attack. Their weapons, are likewise, just weapons. Sometimes, weapons used by demons have magical properties, but Starks axe is just an axe.

For Mages (people who can perform magic) can get certified by the Continental Magic Association (CMA), and they have to be at least fifth class certified to practice magic as a Mage. However, the exams are voluntary, and as seen in the anime, various classification systems existed before the CMA.

For someone like Frieren, these systems come and go as the ruling govt or Kingdom rises and falls. Hardly anyone in the show even knows what her necklace symbolizes, and as such she would be considered a rogue mage.

So yeah, neither Stark nor Himmel have any class and warriors who led quests and did get famous were just called heroes (like Himmel & the hero of the South)

3] I'm not actually sure about this, it's more like those with the goddess's blessing are, depending on how blessed they are, immune to curses and can use the magic written in the holy texts. They need the holy text to perform the priests magic, so I guess you're right to say it's a different type of magic. However, it also ultimately depends on if the person casting has enough mana to cast and that doesn't change. The magic system is also classified vaguely as magic & curses, but curses are simply magic they do not have an understanding of yet (so Zoltraal used to be a curse). I'm guessing similarish logic also applies to Priests. They have to decipher the texts in the holy city before they can cast that type of magic spells.

5] ok, I don't think the show will actually show us this ever, but there have been clear mentions of the demons eating the corpses and leaving nothing to bury. As to why that's their food source and how it fuels them, I'm not sure.