I read that support for Debian 6 ended this month. And here I read that there is LTS until 2016.
Is this for paying customers only? Or can we safely keep using Debian 6?
Debian do not have 'paying customers' as such.
You can safely keep using Debian 6, however only i386 and amd64 architectures will be receiving the long term support.
Additionally, the long term support is not handled by an official Debian team, so the paperwork may not be handled as well as if it were an official Debian release.