I like Marvel comics, although less so the Avengers characters, but tend to dislike the Marvel Studios films. Regardless,
1. I think they're popular mainly from going against the superhero cliches, that superheroes are loved by the public and have a successful and/or stable personal life. The Marvel characters tend to have a lot of personal problems, high costs to being a hero, and otherwise be distinct whether it be Spider-Man and the X-Men having a lot of angst, Iron Man often being less than role model-y, Captain America being willing to go against the government.
With the Marvel Studios films in particular, they often have a light, comical approach to the material, a lot of viewers like that it's not taking itself too seriously, pokes fun at some of its own elements, while also having some serious elements including with the story and social commentary, and a lot of people love that combination and find it very effective; it has some drama and dark element and yet overall feels, including in endings, pretty feel-good, upbeat. And in particular many people found Downey Jr. as Stark and Evans as Captain America compelling, especially that Captain America isn't the stereotypical two-dimensional/simple-minded do-gooder his name and previous reputation might imply.
2. The main effects are probably just adding to the bigger trends of having more unconventional heroes (ones with clear personal flaws, a lot of snarkiness like Jack Sparrow) and more multifilm pretty interconnected series, audiences accepting that in a series there will often be cliffhangers and a lot unresolved in a particular installment (like with Twilight and Harry Potter), also that it's not only OK but good for action movies to involve some social commentary about real issues like mass surveillance (and also OK for the movies to take ambivalent stances).
Also that it's OK, even cool, for superheroes to share the spotlight with other superheroes, sidekicks or not, that big ensembles can work, and that it's positive to have more diversity in the casts (like audiences tending to embrace Falcon, War Machine, later Black Panther, also reflected in the comics Miles Morales and Spider-Gwen emerging and teaming up with Peter Parker in adaptations).
3. Hard to say. A lot of the early success was driven by Downey Jr. and Evans but the success of Ant-Man, Doctor Strange and Black Panther and Captain Marvel shows there's still openness to new characters succeeding. The audiences are probably also still are interested in Hulk and Thor continuing.
A big blow could happen if the viewers get tired of having a lot of snarkiness or crossovers (and/or big ensemble casts) but that's unlikely to happen for a while and the movies could also gradually shift away from those aspects.
4. My favorites are Spider-Man 2, the first 2 X-Men, The Incredible Hulk as well as Batman Returns and Superman 78 and Watchmen. Spider-Man and Batman are my favorite heroes.