I'd suggest starting with the 'Captain America: The First Avenger' comic series. It gives a great origin story and sets the foundation for the character.
Sure. In the comics, after Steve Rogers was believed to be lost or incapacitated, characters like Bucky Barnes and Sam Wilson have taken up the mantle of Captain America at different points.
There has been. Different story arcs in the comics have seen new individuals stepping up as Captain America, each with their unique traits and motivations.