9. Jan 2017: Why I told my friends to stop using WhatsApp and Telegram
Telegram is a tricky one since as I mentioned its encryption protocol shows some flaws from an theoretical perspective. In 2015, a security researcher published a paper revealing several major exploits in MTProto and concluded that Telegram shouldn’t have tried to roll their own encryption.
The author dismisses the Telegram protocol as insecure based on a piece of research that doesn't prove this point.
Was there any Telegram statement? Yes
Update: The blog author already corrected his text and linked to Telegram's statement.
13. Feb 2018: RT Kaspersky uncovers Telegram vulnerability that allows malicious crypto-mining
Cybersecurity firm Kaspersky Lab has uncovered a vulnerability in the Telegram desktop app which allows the social messaging app to be exploited for mining cryptocurrencies.
They make it sound like it was just discovered. The issue was discovered 2017 and fixed immediately by Telegram developers. Also for this to work you’d have to click on a malicious file looking like an image sent as a file (without a preview). Windows (the only affected system) would show a warning, asking if you want to "run this software".
15. Jan 2018: A look at how private messengers handle key changes
The author of the Medium post seems to have little understanding of how things work on Telegram.
Telegram Statement regarding key changes.