***not a teacher***
In 1, when you're mentioning last year it means the action was finished in the past. "I've been elected...' seems to be a piece of news, or of an event which has recently happened.
In 2, 'I've worked for / I've been working' would both be the right form. Here 'I worked there for 5 years' would suggest that for a period of time in the past you worked there, and then you stopped. (Since then you might have had other jobs.)
In 3, again it emphasises that just recently it happened to you, though I suppose in American English a simple past is always preferred in such cases.
Hope you'll get better comments.
Student or Learner