Short answers, pulled from the story.
A party in role-playing games is a group of characters who adventure together. In tabletop games the party is made up of player characters, sometimes joined by non-player character allies controlled by the players or the gamemaster. In computer and online games the composition and control structure varies.
A mule is a non-player character or alternative player-controlled character used primarily to carry heavy or bulky items. The term applies when resource management creates inventory pressure and the character's value is their carrying capacity rather than combat or story contribution.
In single-player computer role-playing games the player generally controls all party members. The degree of control varies by game, ranging from fine-grained orders to each companion to more automated systems where the player intervenes only at key moments.
In online role-playing games the party is made up of player-controlled characters as in tabletop games, but non-player allies are always controlled to some extent by the computer's artificial intelligence. In tabletop games those same allies can be directed by the players themselves or by the gamemaster.
Party members in tabletop and single-player role-playing games are valued for their tactical or story potential. Resource management is a crucial part of role-playing games, and the combined abilities of the group determine what challenges the party can overcome.
Yes. In tabletop role-playing games a party is primarily composed of player characters but can include non-player character allies. Those allies may be controlled by the players themselves or by the gamemaster who runs the game world.