The answer to 1, 3, and 4 are all that they're elements to make you unsure if what they're saying is true or if they're crazy. It just isn't done to great effect.

1. they saw it in their vision, they were doing what the vision showed them.

2. well they're not the 4 horsemen of the apocalypse, they were trying to stop it, hence the change in roles.

3. it's another example for eric NOT to believe them.

4. it's not pre-recorded, it's just re-airing. Like all cable news channel, they loop breaking news. Like eric said, those stuff happened hours/days before (another example for eric NOT to believe them), but Leonard knew when they would re-air it from his visions. Hence his ability to repeat it.

I've read the book that Knock at the Cabin is based on so I'll try to fill in what Shyamalan didn't.

1. The visions described exactly what kinds of weapons that each person would have with them. As you saw in the film, they wanted to follow everything that the visions showed them to prevent the apocalypse. If I remember correctly, in the book, Redmond is the one that builds all of the weapons and that provides them to the other three once they meet.
2. This is just M. Night hammering home the central allegory in case the audience didn't get it. The book does not straight up tell you that the four visitors are supposed to be like the Four Horsemen of the Apocalypse. I suppose assigning each person one of the four titles further drives home the metaphor?
3. It blurs our understanding of why the visitors are there and why Andrew, Eric, and Wen were chosen. If the four of them were chosen by some high power and the selection of the family was random, isn't it weird that Redmond was involved? I mean, it definitely could still happen, but it's an odd coincidence. The book has more little details like this so we as readers (or with the movie, as the audience) are never certain as to what lead these parties together.
4. See Point 3, but also, it's looping news footage the way that any cable news footage would be so nothing out of the ordinary. All of the events already happened hours or days prior to the deaths of the visitors, so it's not like they were triggered by the deaths, but they're happening just as the visitors described.

As with most of his movies, great premise, subpar execution.

One small detail that bugs me is that if they had these detailed visions, why were they surprised that the family was a gay couple? I mean, I guess they didn't get to actually see the family in their visions, but that seems a little lazy.

1. To make the couple stay and listen
2. It was live