Connections & Different Travel Classes

Would anyone know if the system is set up such that passengers can travel on different classes when connecting?

For example, a passenger in economy on a short flight will travel in business or first on a connecting long haul flight?

A first class passenger will use a business class as a connection (not origination), if first class is not available.

Not sure about business using economy on connection. But they only downgrade, never upgrade, and on connections.

So my feeder routes would need to have business & first classes if I want the connecting routes to have more of those passengers?

Yes, if you want those passengers. I see no whatsoever reason to not have business as that is the most profitable class. Personally I dont bother offering first class. 

I offer three classes on ALL of my route, regardless it's being filled or not. Even a short flight of 120 km has First Class seat, and to my surprise, 95% is filled.