<<"On the 19 June timetable, the Interlaken Ost to Zurich HB shows a stopover at Bern arriving at 10:52 on platform 6 and the connection leaves at platform 2 at 11:02. Is 10 minutes enough time to do the connection? What if there is a delay? Do we just plan to take next train? Same situation with Murren to Lauterbrunnen trains">>
Those are good questions, and the answer is different for the two locations.
The usual permitted connection time can be as small as 4 minutes at most mainline stations. Ten minutes is generous for Switzerland. When I check the timetable, i see that you will come into Bern on Track 7, not track 6. However, it makes little difference. You should have no problem with a 10 minute connection, even though Bern is a very busy station. The underground passage beneath the tracks is very wide and handles heavy traffic well.
To be more sure,especially if you have chosen to bring your luggage with you, you might try to be near the middle of the train when it comes into Bern. There is not a "dead end" railhead; the trains can come and go from either end of the station.
If you miss the 1202, I'd wait for the 1232. Nonstop fast trains run every 30 minutes from Bern to Zürich. There are several other trains per hour, some of which are slower and make stops or have change of train connections, which will show in the time table. Check Bern to Zürich for that date and time.
I know that there is a map of Bern Hauptbahnhof somewhere on the SBB web site, but this one was handy on my computer:czech-transport.com/images/Bern-train-station-plan.pdf
The train from Mürren to Lauterbrunnen has two stages - along the plateau to Grütschalp, then down to Lauterbrunnen. There are only a few trains per hour, and they may vary by a few minutes, but no more than a few. Without studying the time tables carefully, I don't know if they are timed to make connections at Lauterbrunnen.
I think it likely that there is some flexibility there, but the trains from Lauterbrunnen to Interlaken Ost will be timed to make connections at IO. They will leave Lauterbrunnen promptly. The connection at the end of that train ( at IO) is the one where I have had to hurry - that is, inbound from Lauterbrunnen and outbound to Bern. It's been a few years, but the stairs and cross-track pedestrian tunnel were crowded with slow people with luggage in a small space. That maybe better now. Look it over when you are inbound to see what it will look like outbound. I'd check that one.