It means certs signed by Let's Encrypt will work just fine for people without any special setup. See https://helloworld.letsencrypt.org/ for an example.

This does not, however, mean that we can all start using Let's Encrypt. They're doing a slow roll-out before making certs generally available to the public. You can apply for the Beta at https://goo.gl/forms/kf0IGCeAk5, or wait until general availability later this year.

"Yes", except that general availability doesn't come until the week of November 16th.

In a word, yes.

When a server uses a Let's Encrypt certificate, a browser will consider it as issued under an IdenTrust root CA, which the browser trusts. So it will consider the Let's Encrypt certificate trusted.

Yep, if you get a certificate signed by one of their intermediate certificates, you're good to go.