What the green dot means
A green dot on a member's profile means they're online right now. It's a good time to send a Like or a message.
Can I see when someone was last active?
No. You can't see the date or time a member was last active. The green dot only shows that a member is online right now. If you don't see a green dot, they aren't online at the moment.
Can I hide that I'm online?
Not at this time. Turning off Discoverable stops you from being shown to other members as a new potential match, but it doesn't hide your online status. See How do I manage my profile visibility?