Echoes is a remake of an earlier fire emblem game from before the weapon wheel. The story of the original game was better than most of its time but many things about the system were unbalanced, impractical, and all around made it a pretty bad experience for the players. They made this as a kind of anniversary game for the Fire Emblem game and a throwback for old fans by doing a major re-balance while still keeping some of the elements that were prevalent in that era of Fire Emblem games. Honestly, if they add the weapon wheel into the game again it's a huge improvement from their current series. They probably used it as a test run to see how people reacted to it since their next FE game (three houses) seem to be using a lot of the mechanics from it while further polishing the game.

- - - It is a remake of an older Fire Emblem game, including mechanics. They... didn't bring back a lot of these mechanics for a reason. - - -

Answer 1) Skills are learned through weapons and class rank ups I think. There were no skills until Awakening I think, but there are mods for GBA roms that actually add skills to the older games like Rekka no Ken and Sacred Stones. Fun fact right there. Answer 2) Villagers can promote into pretty much any class in that game, so they all start out as them for versatility. That being said, most of the villagers excel in certain classes, like Kliff as a mage for instance, so people tend to only go with one class with them all anyway. It's the thought that counts I guess? Answer 3) ... *Shrugs* I dunno.

To add to what Gin said: Skills have been a thing since Genealogy of the Holy War, they were removed in the first two GBA games, but some were clumsily added in The Sacred Stones as class-exclusive fun stuff that doesn't work half the time. Path of Radiance was the first game to be released in the west and have the skill mechanic we know now.