Connecting sounds good, but it must be used with care. In my mind 'connecting' makes some warranties regarding scheduling and waiting time. This is a very useful distinction to maintain.
At the very least a genuine connection implies both repeatability (through headway harmonised timetables) and a waiting time appropriate for trip type (e.g. 28 minutes is too tight for flying, terrible for suburban transit but probably OK for between two [inter-city] trains).
Absolutely. An acceptable connection time is short enough that the whole trip still feels fast. In general, the further you're going, the longer a connection time is tolerable. (The same is true of waiting time at the start of the trip.)
Apart from scheduling a connection there may also be an obligation to honour it, even if services are running late.
Where neither level of connectivity is provided, and service is not frequent enought to render it meaningless, I don't agree that we should claim these services are 'connecting'.
Here in Melbourne we seem to use 'connecting service' in circumstances when 'intersecting services' might be more appropriate (ie a guarantee of physical access but no warranty regarding the transferred to service 'connecting' or even operating.
Peter goes into more detail in a post of his own, with useful Melbourne-specific detail that I've edited out of his comment here. But it's not just Melbourne that represents intersecting services as connecting services. I've seen many low-frequency suburban systems that present two routes as connecting if they serve the same spot, even if they aren't even running at the same time of day, let alone timed for the connection. Peter's right; where two routes intersect, but no self-respecting person would connect from one service to the other because of (a) an unreasonably long wait or (b) inadequate reliability, these should be called "intersecting," not "connecting."
'Intesecting' sounds cold, clinical and like lines on a map. However we do need something to differentiate it from connecting, which should only refer to services with genuine timetable co-ordination and (possibly) even guaranteed connections where services are held back. This is where 'change' is good as I don't think it implies a scheduled connection as much.