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.
This is not true, it is available in the open-source Telegram clients.
What you probably mean is that it is using an unusual and not well studied encryption algorithm. This means you need to be a real cryptography expert to spot flaws in it.
Telegram justifies this with a bit of FUD about well known encryption algorithm being NSA sponsored etc, but when cryptography experts did look at Telegram’s homegrown algorithm they were less than impressed.