Where is Telegram for Android developed? (Or: is it really free software?)
The App is free and will always be.


  Telegram is free and will stay free — no ads, no subscription fees, forever.
  - Telegram FAQ


Apparently they are not updating the code right after each release, but after a month or two they do (Usually.)

To submit a bug you can Contact Telegram Support within the app, Settings >> Ask A Question.

In short: It is a free software, And its somewhat open source...