Hi Sameerg -
That is a lot to cover in your short trip, even if "cover" means look at it briefly while passing through.
What to see depends a lot on personal opinions. Here are mine:
Titlis, Pilatusare best seen from Luzern, which is nice in its own right.
'Swiss Alps" covers a lot of territory. The Alps are visible from many parts of Switzerland. There are also "Bernina Alps," "Uri Alps," " Valais Alps," etc. All part of the "Swiss Alps" in different parts of the country. So, you'll need to think about that as you plan, and keep an eye open when you are there at many of the places you have names. Luzern is in the Alps. Zürich is not.
I have attached a couple of images from places quite distant from the Alps. Some are from the Emmental, well to the north and between Bern and Luzern, some are from near Neuchatel and Ligerz, in the French -speaking region near the French border in the west. They show how the Swiss Alps are visible from many places.
In early May there will be a lot of snow in the Alps, and many tourist services - such as quite a few of the hotels, and most "ski" lifts or excursion cableways will not be operating. The snow is of poor quality for skiing, and there are not a lot of skiers to spend money in those months. For example,the cableway from Wengen to Männlichen, where a famous easy panoramic walk starts, only begins service on about May 24th. The trail itself typically does not open until early to mid-June.
The cograil to Jungfraujoch does run all year. It is expensive. Weather near the Jungfrau is notoriously changeable, especially in late Winter and Spring. Forecasts re only good for about 24 hours in advance; maybe a bit more. So, if you want to go up to Jungfraujoch, you improve your chances tremendously by staying in the region for more than one day. Two or three days is best. If you go up when there are clouds around the peak, you pay a lot to see the inside of clouds. Boring.
It is possible to take an early train from Luzern, go to the Jungfraujoch and return, in one very very long and tiring day. At least one forum visitor has said that it is worthwhile. The train ride is reasonably scenic, too.
There are many ways to find out about the weather near/at the Jungfrau. If you are in Luzern, you can ask at the Tourist Info office by track #1 in the main station, use the TV in the early mornings, or check out webcams.
The links I gave above will help with many ways to keep an eye on the weather.
We are now about to get into personal opinions.
My opinion? You don't have time to include Geneva or the lake and still do justice to the other things you want to do. Lake Lucerne is wonderful.
There are images of Lake Lucerne (in German, der Vierwaldstättersee) in these links:
Also, some attached.
And the Rhine Falls, though at their best in the Spring, with snow melt and Spring rains, are not all that different from waterfalls all over the world. Powerful, but not very high. I prefer to spend my time on things that are uniquely Swiss...Luzern and nearby, day trips from Luzern to Bern, Zürich or Basel (if you want to see those cities or have bad weather) and the Jungfrau region.
Although it would not be impossible to reach the Bernina Express, it is a long way from central Switzerland and the Bernese Oberland. I think it is too far away or takes too much time out of a short trip, compared with other options.
Have you looked at a map :
Zoom in for train lines; in the menu under "Points of Interest," you can turn on "traffic" for transport stops.
And have you used used the timetable to get an idea of travel times?
These links may help you better understand the region:, especially, the Jungfrau part of the Bernese Oberland:
www.swissholidayco.com /Public/Assets/User/fi les/Map-of-Jungfrauregion1.jpg