Adding to my earlier post -
<<"My rough plan is Wengen->Mannlichen->Kleine Scheidegg->Jungfroujoch. I assume this can be done in 1 day(?).">>
In the Summer, that is correct. Depending on when you start, and how long you spend up at Jungfraujoch, you could a few hours left at the end of the day.
The Männlichen to Kleine Scheidegg trail is available for hiking in the Summer and Fall, and is groomed for hiking during the main part of the ski season. However, as the weather gets warmer -- roughly in April, depending on how warm it gets and snow conditions - the snow for skiing is not as good, it is more difficult to maintain the trail safely, and there are fewer visitors. Trail maintenance is discontinued until some time in the June time period mentioned. So, right now, the trail is normally open. It is also closed in early Winter/late Fall, and opens in approximately early to mid December.
I do not know exactly when maintenance will stop for the season, but it is possible that the trail might still be accessible in the earliest part of April. Hotels, train station staff, and tourist offices in the region all keep close watch on the conditions. They can help you.
Arno gave you links for the weather. In the Alps, it can change quickly, and it can be brilliantly clear up top while cloudy or foggy at low levels ( or, vice versa). (See attached images showing each variation, from mid-December 2016. Even with the conditions as shown in Fribourg about 50 km from Interlaken, at low altitude below the cloud deck, there were clear and sunny regions in the not-far-distant Emmental between Bern and Luzern).
It is difficult to predict the weather and sightseeing conditions with accuracy even two days in advance. So, it is wise to have contingency plans, in the region....such as visiting Brienz and the woodcarvers shops ( Jobin is one of the best) or Bern. Even Brig, since the Rhone Valley can be sunny when the rest of Switzerland is not. It is not uncommon to find extensive sunny periods on days when some rain and clouds are forecast, and due to the geography, regions only a few kilometers from each other may have different conditions almost anywhere in Switzerland.
2.- Jungfrau region and Bernese Oberland -
It is clear that you have done some reading about the region.
The two days of trips that you mention are good ideas, and can easily be fit into one day each as long as the cableways are running and the trails are open, with plenty of time to look around, if the weather is clear.
However, just to be sure that you have seen them, here are some links to consider for your other day or for contingencies -
These links can tell you more about the region, and the map and timetable linked earlier in the thread can help you understand how easy it is to get to Bern, or other options. Even Luzern is a possibility, but it is 1 hour 51 minutes each way from Interlaken Ost , via the rather scenic route over the Brunig Pass ( via Meiringen). Add time to/from Wengen if you stay there.