In the following example only - how many segments are flown?

JFK
United to Heathrow
LHR
Own transport (EG Eurostar) to Paris
CDG
Singapore airways to Singapore
SIN
Singapore airways back to New York (via change of plane in LAX)
JFK

These airlines probably don't fly these routes in reality. Is this 4 segments?

I know the surface milage is counted from the maximum allowed under the fare but does it also count as one of the 15 segments?

Or do they say you took three 'sets' of flights so three segments used?

Julian