There is no alternator symbol or light on the 2013 if i recall its just the battery light which can beIt doesn't sound like an alternator. You don't have the alternator light on the dash too do you ?
Sounds like your dodgy charger or socket might have tripped a fuse on a control unit. They're not physical switches. Because all of those things that aren't working are controlled by a single control unit. You've got a red triangle. Get it plugged in.
You could try disconnecting your battery for 24 hrs too. They might reset.
Duff battery / failure of the charging circuit / alternator regulator fuse blown