1. Yes, I'd say that you need a new battery. (They are expensive!)
2. No I don't think that leaving the battery in and on charge has any detrimental affect.
Experience with my last three Laptops has been that 3 years is the maximum battery life experienced.
My current Dell laptop shows a fully charged battery. In use it lasts for less than 25 minutes and then collapses suddenly, shutting the computer down. The Laptop is less than three years old.