It basically means that only the sender and the intended recipient can actually read the message. This is in contrast to the usual encryption that is only used to secure message from the sender\receiver to\from the server.

It is important though that there are a lot of companies that don't use Cryptographic terms correctly. Though at least for the large direct messengers (e. G. WhatsApp) they usually do use the term end to end encryption correctly.

None that we know of. However there are some standardised cryptographic algorithms that have weird, unclear design aspects and we are wondering if these could be back doors we just don't understand yet. In same cases these aspects have also been shown to be insecure but we have no proof that this was intentional.