Hi Lakshmim -
In mid April, you are in low season. Skiing has pretty much stopped, and hiking (Summer season) is still 2 months away.The cableways are generally not running. Grindelwald to First is not running.
Wengen to Männlichen is not running.
A hotel that I stay at has these open seasons:
<<"Winter Season 18.12.2015 – 28.3.2016
Sommer Season 3.6.2016 – 9.10.2016">>
Many but not all restaurants and hotels will be closed.
Sunset is at 2010 in Wengen on April 13th
The cograil train is running...Lauterbrunnen to Wengen to Kleine Scheidegg thence Grindelwald, with the expensive branch to the Jungfrau.
It is impossible to predict the weather for mid-April dates at this time. And, it is very changeable from day to day or even during any one day in the mountains. The weather could be beautiful or awful. In April, there tend to be more cloudy and rainy days ( or even snow at higher elevations) than in summer and early fall. But, in April 2014, there was a whole week of wonderful weather over most all of Switzerland, and I was able to take the attached panoramic photograph. Very unusual weather.
Note the snow on the Alps, and that the trees are flowering with no leaves on them yet. The grass is just starting to get green. Elevation 700 meters in an area that gets sunshine. (The Lauterbrunnen Valley is deep enough that sunshine hours are more limited.
Basically, you will need up to date information on the day you plan to hike or the day before.
Even the valley floor may not be free of snow, but you could probably walk from Lauterbrunnen to Stechelberg ( Bus stops a long the way and bus for return).
Grütschalp to Mürren would probably be cleared for walkers.
Arno and Annika have much better detailed knowledge of the seasons in that area; perhaps they can refine my comments.
<<"Please suggest an itinerary. ">>
Arno has already suggested a useful link in his post above.
They are also the experts on rail passes. I'm not knowledgeable about the various discount passes.
Whether you should go there at all is a matter of personal preferences. The area will be impressive at any time of the year, even in mid April, which is not the best time, by far. A ride on the cograil part or all the way along its route could be rewarding, if the weather is clear, but it is not a hike.
With my own perspective, probably because i have been there many times, I'd stay in the Luzern area and not make the trip, because it is a long trip for only a short time in the Jungfrau area. But, for a first time visitor, the judgement could be different. And, the train ride to and from is scenic, assuming clear weather.