Hi Roger and Rosanne,
Welcome to MySwissAlps! Somehow your itinerary didn't get attached, but I will respond to a couple of your questions in the meantime.
>> We have a trip planned in September in Switzerland.
... Will any of the cable routes be closed then?
They should all be operating in September. Generally speaking, mountain transport that doesn't operate during winter stops running in the second half of October and reopens around mid-May. Those that operate year round tend to close for maintenance twice a year, in April/May and in late October/November.
>> Wouldn't it be better to take a direct train from Bern to St. Gallen than go through Zurich?
Depends :-) When travelling with luggage, a direct service is generally more convenient.
Services from Bern to St. Gallen run twice an hour. Those leaving Bern at 2 minutes past the hour require a change in Zürich. Those leaving Bern at 32 minutes past the hour go direct. So it depends on what time you want to leave, and whether it is worth waiting half an hour for a direct service if you are ready to leave earlier.
>> Do any of these train routes require reservations?
Without your itinerary, I'm not sure what trains you are referring to, but here is some general information.
Reservations are compulsory for the Glacier Express, Bernina Express and Gotthard Panorama Express.
Reservations for the Golden Pass panoramic route are not required, but can be useful for the sector Zweisimmen to Montreux in busy times.
Reservations for other trains within Switzerland are not needed.
>> Is it better to stay in Lausanne or Montreux?
Montreux is smaller, more picturesque, and more conveniently located for activities in the Lake Geneva region. Also, Montreux main station is only a short walk from the boat wharf, making transfers between train and boat very convenient. However, it always comes down to personal preference.