Mobile apps for android and iOS
Desktop app for MacOS, Linux and Windows

Yes, it supports markdown.

You can download and use it as free for self-hosted server.

Almost all features of Slack are available in Mattermost.

You don't need to rely on someone else's servers, you can host Mattermost on your own server.

With Docker set up, you can install Mattermost with the following command:

docker run --name mattermost-dev -d --publish 8065:80 mattermost/platform

For other cases, installation instructions can be found here.