we've installed the ADO app but there is not much info coming from it! One would expect the biggest bus company has a proper working app!But well, thats me...
How can you find out bus schemes of all bus destinations to major cities and towns in Mexico? We prefer to do this online instead of going to the busterminal.

Not knowing what you know about Mexico bus systems, not all carriers serve the entire country/major cities. For example, ADO, from Mexico City, primarily serves the southern part the country & the Yucatan. ETN & Primera Plus, Central part of the country. With that said, if you're looking ahead more than a month or 2, you won't see schedules. But they rarely change, so what you find for a week out will very likely be the same in 3 months.