is my charger working?

[dj1]

Now that it's getting cold I decided to try out my new Porsche cig. lighter trickle charger(the small transformer unit). I've been driving the car about once a week so I figured the battery is pretty well charged, so i was surprised to see the charging light still on after 12 hours. Here's my questions:

1. how long should it take to bring up a good battery to full charge?
2. could there be a problem w/the cig lighter fixture...and how would you check that?
3. can leaving this thing plugged in and charging constantly damage the electrical system?

Thanks for your input! DJ