I recently switched from Whatsapp to Telegram, mainly because it has self destructing messages, but the features you want, and extra are also here:
- Android and iOS and Windows Phone and OSX and Linux
- End-to-end encryption1
- Group chats (up to 200 people)
- Free, no subscriptions, no ads
- Uses phone numbers (like Whatsapp)
- Over the internet
- Use on multiple devices (unlike Whatsapp)
- Send self-destructing messages (in secret chats, see below)
- Mostly open source
In Telegram, there are 2 types of chats - normal chat, and secret chat.
Normal chat: data is in the cloud, encrypted
Secret chat: data does not stay in the cloud once delivered; end-to-end encryption; Diffie-Helman Key Exchange
If you want to know more about the technical details, see the FAQ for the Technically Inclined, or just the regular FAQ.