And if you block pings to be "stealted", there are other ways to find out if your computer is "up"
Yes, but most people don't bother probing further. Unless it's someone that is intent on getting onto your computer, in which case even a firewall wouldn't stop them 100%.

Anyway, I won't change my mind on the firewall thing. I know a couple of people whose machines got cracked into, and neither had a firewall. It's just sensible. On the other hand if your router has a firewall on it, you don't need one for your computer.