A lot of your questions, including whether to book the various special trains, will be answered here:
To understand timing, you can use the timetable.
If you enter Luzern ( local German spelling) for the beginning and destination Montreux in the timetable, it will default to the fastest route, which is not the Golden Pass route.
It is possible to string together the entire set of trains on the Golden Pass Route, but I find it simpler to split the journey sought in the timetable and use it twice -
Once for Luzern to Interlaken Ost, where you could use "Meiringen " in the "via" box. However, since it is the fastest route, ( 1 hr 50 minutes) you will automatically go through Meiringen. The route through Bern takes about 2 hrs. and 20-30 minutes.
Then enter Interlaken Ost to Montreux, in which case it is important to enter "Zweisimmen" in the via box. Otherwise, you'll go through on the short faster route on mainline tracks via Lausanne, Bern, Olten to Luzern. That fast route takes only 2 1/2 hours. more or less.
The trains of the Golden Pass Route from IO to Montreux take from 3 hours 5 minutes to 3 hrs 44 minutes, and do not run as frequently as the trains on the short route. Then add that the trains of the Luzern Interlaken Express on the Golden Pass route via Meiringen take about 2 hours as noted above. If you can fit together the connections that let you take your preferred type of train between Montreux and Zweisimmen, you could do a round trip in one long day. Minimum, about 10 hours, with no time in Montreux.
It is helpful to look a this map when you consider your routes:
If you zoom in, you can see the rail lines.
If i were doing it, I'd take the Golden Pass train to Montreux that matches my interests, then return via Lausanne Bern (sometimes through Olten - depends on the train) to Luzern.