Hi Monica -
It is nice to work with someone who plans so carefully. If I don't do something similar, especially on jet lag days, I find that I waste a lot of time making decisions (or trying to make them).
1. In order to visit Mt.Titlis, where do we disembark? Is it at Engelberg (Talstation Titlis) or Titlis?
My Swiss Alps has a page for Titlis which gives those details:
Talstation means "valley station" which is the general name for the last (bottom) station on mountain transport. The top end is the "Bergstation" (mountain station).
The end of the train service from Luzern is at Engelberg.Then you need one of the mountain services. You walk to Talstation Titlis, nearby, to go up. So, the name Engelberg (Talstation Titlis) implies that the Talstation is nearby the Station Engelberg.
2. Do we have to board a boat to get to the Transport Museum or can we use any other means of transport as well?
You can take a boat,bus/tram or train.
Mouse over the icons at the museum on this map, and you will see the bus/tram line numbers (which are 6, 8,24, and N4):
map.search.ch/?pos=668228,211675&z=51 2&poi=bergbahn,haltest elle,museum,parking,vi asuisse,zug
The museum is at the magenta building icon close to the word Brüelmoos.
I have a moderate interest in trains, and found the historical information about the Swiss system, particularly in the Alps, quite interesting.
If you have time, the walk to or from the museum along the shore back to downtown is about 1.5 or 2 km and is very nice. Mostly or all parks.
This map shows that it is a Wanderweg ( yellow line) so it will have signposts. You would not need them.
map.geo.admin.ch/?topic=swisstopo&lang=e n&bgLayer=ch.swisstopo .pixelkarte-farbe&catalogNodes=139 2,1538,1396,1430,1436& layers=ch.swisstopo.sw isstlm3d-wanderwege&E=2667410.1 5&N=1211885.88&zoom=8
<<"I was able to get in touch with your friend and hopefully I'll be able to see him in Sachseln.">>
Glad to hear it. He let me know. Some years in the past he was a helper in Switzerland for travelers with a tour organization. So, he is quite experienced in answering questions and providing advice about Switzerland.