>> We have no idea how big the stations are and how easy or how difficult it would be to change platforms within that time.
For the bigger stations, you can get maps of the station and platform layout:
Under the heading Equipment and mobility at the station, you can confirm whether there is step-free access to platforms (lift/ramp). I would expect that all stations at which you will need to transfer will have a ramp at the very least, so you won't have to contend with steps to slow you down when travelling with luggage.
You can also see where steps, ramps (and lifts/escalators if available) are located along the platform, which is divided up into segments denoted by letters of the alphabet on a blue-and-white sign overhead.
>> Also, we will have to take an early morning train from Lucerne to Zurich Airport on the day we return as our flight leaves at around 9am. Hence we must ensure that we do not miss any connecting train. Do you have any tips to offer that would make us feel confident and we will not miss the connecting train ?
I would get a direct train from Luzern to Zürich Flughafen (Zürich Airport), avoiding any transfer at Zürich Hauptbahnhof (Zürich main station). Zürich is a big and busy station, and I often get a bit disoriented in the underground areas there, despite having been through it many, many times.
>> 2) When we are travelling by cable car or bus, and buying tickets on the spot, do we need to have exact change in CHF to pay for the fare ?
You can usually pay for cable cars by credit card. You don't need exact change for bus fares if buying from the driver, but carry CHF 5 coins or small denomination notes as a courtesy.
>> If we have to pay cash (if credit card is not accepted), will the machine or the bus driver return the change if we do not have the exact fare ?
Yes, but carry small denominations as a courtesy.
>> Also will the half fare be applicable even for short bus rides and boat rides in Lucerne ?
No. For short, inexpensive rides, the fare will usually be a bit more than half-fare.
>> Should be buy two individual train tickets online or one ticket for the two of us ?
I don't know whether you can put two people on one ticket, but I would avoid doing that anyway. It's better for each person to carry their own ticket (and passport etc) in case of loss, theft, or getting accidentally separated.
>> 7) Schilthorn Piz Gloria website also offers tickets between various locations and Schilthorn. Would they be different in any way than the ones I can buy on SBB or STC website ?
I wouldn't think so. Can you be more specific about what tickets you are referring to?