Hi Clifton -
Welcome to My Swiss Alps.
That sounds like a nice trip. I have traveled those regions in April, and , they can be quite pleasant, especially at the lower altitudes.. Plenty of Spring rains, of course.
The Swiss are famous for the quality and timeliness of their train service. Your questions about reliability would be puzzling and amusing to the average Swiss...just joking..;-). To be serious, you can rely on the trains 100%. You will be amazed at how well the entire travel network serves various types of travelers.
The timetable will help you with planning:
Read the instruction page, please.
Here are some other useful links-
and links contained therein, such as:
Altitude is really important for weather and travel conditions, especially in Spring and Fall.
Have you checked out a map? This one is very good for Switzerland -
Without knowing more details, and your particular interests, I'd not have much to say about your routing.
Maybe I'd do the northeastern section first, and head south from Luzern.
In early April, Spring is just getting a serious start at the lowest altitudes. In the high Alps, it will be late Winter, and Alpine pass roads don't open until the snow melts sufficiently to clear them in early June. Alpine resorts tend to close down in April because the skiing is not so good; they reopen for Summer season in early to mid-June.
I have attached an unusual picture, I (took it in mid April, 2004). I was in the Emmental at about 700 meters elevation, overlooking Sumiswald and Trachselwald. Switzerland had an amazing and unusual stretch of about one week of warm, dry, sunny weather. Not at all typical of April. More like late May or June. In the picture, you can see the the trees are just blossoming, the grass has not really greened up except in the lowest areas,and the Alps have plenty of snow on them.
There are tunnels that are open all year on main north-south passes.
However, I'd certainly agree with your decision to use the trains. Everyone can look out the window, and service is frequent.
Rail passes can cut your costs. Best to think about them after you have decided your itinerary.