Responsibility is easy. Just have them do their homework and it maxes out naturally.
For empathy, you can do volunteering (which is time-consuming, but available for both children and teens) and have kids play with the doctor playset.
For manners, just have them wash the dishes a lot, and set the table if you're inclined. I think teaching kids to say thanks and sorry should help.
Emotional control, you can have them write in their journal, or do activities that help regulate their emotions like playing music.
Conflict resolution is difficult IMO. There aren't a lot of activities that directly increase it. But then, I don't think it's that useful anyway, so I don't bother with it.