for #3 -
Use the timetable:
Use Luzern as your start, Interlaken Ost as your destination. Set "arrival" in that choice. Enter 1000
On a random day in September, I find trains leaving Luzern at xx05, beginning at 0605, arriving at IO 1 hour 49 or 50 minutes later.
For 1000 arrival, you can take the o805.
From there, using the 0805 departure fomLuzern, you can reach Jungfraujoch at 1205. The connections are generous ....20 minutes at IO, 12 minutes at Lauterbrunnen and 10 minutes at Kleine Scheidegg.
If you learn to use the timetable, your stay in Switzerland will be much easier. Please carefully read the instruction page at the My Swiss Alps link given above. There are some important details there.
The journey all the way to Jungfraujoch is expensive; the last leg in particular. If you arrive at the top and find your self in the middle of a cloud, you will have an expensive view of the inside of a cloud. Not very scenic.
So, please keep track of the weather, and, make sure to check once you arrive at IO. There are other destinations in the region if JFJ is socked in.
The weather in the high Alps changes quite rapidly, and comes in layers. It may be clear up top while it is cloudy or foggy at lower altitudes, or vice versa. Forecasts are not reliable more than 48 hours in advance, and even at 24 hours, may not be 100% reliable.
In September, the lines will not be long at Kleine Scheidegg. Arno or Annika know better than I, but I think you could wait until you get to IO, or possibly even KS before you buy your ticket for the last expensive stretch. Rail stations near the Jungfrau, including IO, have up to date information, and I'm guessing that they will have a webcam running.
There are webcams.