About MTR stations

Any revenues generated not from selling tickets are non-fare revenue (business). Most of the non-fare revenues come from advertisements, like the advertisements on the walls, inside the trains etc. Other main non-fare revenues come from the shops rented out inside the stations. As far as I know, all countries with public transportation have some sort of advertisements. So there are too many to list for your 2nd question.

If you have a wedding party in Hong Kong, you can rent a tram as a float(花車) from the HK Tram company(香港電車公司). That is one non-fare business MTR can think about. Also, MTR can rent part of its halls inside the station for exhibitions. They can also consider selling MTR related souvenirs too.

Coming back to your 1st question. Without any context, your own explanation is probably right. So it is a way of allowing passengers to hop from one type of transportation to another, like from MTR to buses, ferries, mini-buses, trams etc. But on the broader sense, it can also mean a way for people to connect with each other. I often hear people like to take MTR stations as an venue, like "We'll meet each other at MongKok station at 3 pm near exit C" etc. That can also be connectivity too.

This is more like a questions about ideas than a question about English, right ? Do you work for MTR ?

In order to attract people taking MTR instead of other means of public transport, it is necessary to provide 'connection' service to 'connect' people from remote areas to the MTR station. Examples are green minibus, free shuttle and similar.