@Aleksandar Ilic Compose works on declarative pattern to build UI. According to you question we can use Compose to share your UI with multiple platform (Android, iOS, Desktop, Web).
Here's my thought on your questions :
1. Compose doesn't support Over-the-air (OTA) update like flutter through
ShoreBird.
2. Currently there are two option's to create and distribute Desktop App using
Gradle System &
Conveyor
3. Auto-start is system specific component - Nothing to do with Compose API.
4. Again Background processing or communication is system specific component - Nothing to do with Compose API.
5. You can refer
this template to get started with Desktop App and evolve and improve app architecture further more according to project use cases and requirements.
(This template was not maintained actively so consider some changes here and there).