<<"How long / strenuous is the hike to the church?">>
Hi Mike -
Read the text on composite #2.
Here is a highly detailed topo map of the Bielersee shore by Ligerz:
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&E=2576903.7 2&N=1214902.58&zoom=11
Switch to aerial view if you wish. Zoom out for the overall environment of the region. Several of the towns are nice to walk around in. Le Landeron, in particular, but it is a bit of a distance from the train station.
You can clearly see the funicular on that topo map
It runs once per hour in Winter, twice per hour in Summer. Check the timetable for your dates. The Bergstation is named Prêles/Prägelz. They speak German at the bottom; French at the top. You are exactly on the Röstigraben. The climb is steep but short, so if you happen miss the funicular timing you can make the climb, perhaps with a few pauses. Paved.
The upward journey is synchronized with train arrivals. People get off the train and go very quickly to the funicular. Ticket machine is at the train station, on the street side, not at the funicular. If you have a Swiss travel pass, no problem. Sometimes tourist buses arrive just before departure. The boat landing is several meters further away from the funi, and lower, at lake level, of course. I'd not dawdle, or maybe I'd plan to catch the next one if it is on the 1/2 hourly schedule. The trains in each direction along the lake shore run once per hour, and both stop at Ligerz at about the same time. There is also a peculiar gap in the train or lake boat schedule, as I recall. One particular hour of the day, I think maybe that the boat stop is skipped. Check the timetable.
If your friends from Morges wish to meet you there, I can recommend the Hotel Kreuz for a meal. Simple menu, excellent kitchen. Herr Mettler is a very good cook. Frau Mettler's family own some local vineyards.
The funicular is one of the newer single-cable types, and the operator has been known to run people up to the Pilgerweg between regular trips, if he is around. He volunteered that service for me one time when I had a sore leg.
If you wish to ride the funi down from the Pilgerweg, make sure to push the "Halt an Verlangen" button not long before the car is due, or they'll wave at you as they pass you standing by the station. I pressed it once as the car went up the hill above the station, and it re-set before it came back down. Did not stop. The trail crosses the tracks there, and sometimes people are just waiting for it the car to go past. The church is supposed to be unlocked during the day, and is definitely worth a look inside. I know about it because friends were married there many years ago.
Late May, early June is a good time to walk that stretch of the Pilgerweg from Ligerz to Twann. However, it can get very hot in the sun, even then, and it would likely take too much time out of a day trip.
When you look at the map , slide it along the shore line to the left for Schafis. It is close to Ligerz. Betwen the two, there is a lot less territory to cover than at Yvoire, and it is not as prettified.