Becoming captain in player career mode

Unfortunately, at least to my knowledge, there is no Online Career Mode for FIFA 15, nor have there been in any previous FIFA installments.

There are however a couple of Online (PvP) modes that support co-operative play. One of which is Pro Clubs, in which, you and a number of friends create a team. The players in this team comprise of AI and Virtual Pros (which is basically a player you create). In this game mode you take on other people's teams in an attempt to reach Division 1. You can also compete in cup events that happen once or twice a month.

The other game mode is Co-Op Seasons, in which you and a friend (I think this is limited to one other player only, not sure though) play as any team on the game, and you play against another co-op team playing as another team. The aim is the same as Pro Clubs, in which you try and reach Div 1, along with the optional cup windows.

In both game modes, Matchmaking is customised according to what Division your team is in; so people in Div 10 wont be put against people in Div 3 for example. And in Co-Op Seasons, Matchmaking is also calculated against the team you select's star rating; so you won't get Accrington Stanley vs Barcelona for example.

More information on Pro Clubs and Co-Op Seasons

You can practise them, but there is not a mode for just playing them like in the older versions.