Yes, but they take steps to ensure they cannot easily be forced to decrypt chats via a court order in a single country. From the Telegram FAQ:
To protect the data that is not covered by end-to-end encryption, Telegram uses a distributed infrastructure. Cloud chat data is stored in multiple data centers around the globe that are controlled by different legal entities spread across different jurisdictions. The relevant decryption keys are split into parts and are never kept in the same place as the data they protect. As a result, several court orders from different jurisdictions are required to force us to give up any data.
https://telegram.org/faq#q-do-you-process-data-requests
> Furthermore, they frequently "ban" channels that they deem contain "inappropriate" or "adult" content. Clearly they're reviewed by either humans or AI of some sort. So... that makes me uncomfortable.
AFAIK messages are only forwarded to Telegram support if they are reported by users. Chats spreading pornographic content are often banned on iOS due to the App Store guidelines (and in certain countries due to local laws), but illegal channels (e.g. CP) may be blocked globally.
> Also, this means that anyone who has your phone number is told you're on the app and given your username, which you may not want for privacy reasons.
This is not true anymore, a while ago they added new privacy settings that allow you to prevent others from finding you unless they are in your Telegram contact list. (Of course, this means if you don't want anyone in your phone's contacts to be able to find you on Telegram, you should deny the app contacts permission.)