Blog post by crypto professor Matthew Green, discussing what Telegram does (I wasn’t familiar with it) and criticizing its cryptography. He says Telegram by default is not end-to-end encrypted. It does have an end-to-end “secret chat” feature, but it’s a nuisance to activate and only works for two-person chats (not groups) where both people are online when the chat starts.
It still isn’t clear to me why Telegram’s founder was arrested. Green expresses some concern over that but doesn’t give any details that weren’t in the headlines.
As far as I know, nothing in the protocol prevents the server from connecting who is talking to whom. In fact, given that the phone number is how an account is identified, the server effectively has to do this in order to pass messages between people.