7 days in Switzerland for 1st time traveller

Coming from Salzburg, you are going to get to Zurich first because that is where the Railjet train ends and all the connections to elsewhere in Switzerland (at least the ones you express interest in) begin. So you could do it then or later. It is only a 1 hour train ride to Luzern from Zurich.
Luzern to Interlaken is a short trip over a very beautiful mountain railway. Where you choose to stay is up to you. I gather you have already heard that late April and early May is not the most ideal time to visit the Swiss Alps. Sometimes opportunities don't present themselves at the most ideal times, but we just go ahead and do the best we can. If you want to go to the Jungfraujoch, you will need to keep an eye on the morning weather, and if it is clear, go immediately and hope you get there before the weather changes, which mountain weather does quite quickly.
Zermatt is also easy to get to in a half of a day from Interlaken area. Weather again will dictate how much you see.
The 8-day Swiss Travel Pass might be worth it to you. it is not always the cheapest product, but has its conveniences, including not having to purchase train tickets for the most part. You will get a discount on high mountain journeys like the Jungfraujoch and the Gornergratbahn in Zermatt. It also includes free public transit in cities, like Zurich and free admission to most museums.

Since it's low season, will it be advisable to stay in Interlaken or at the mountain village?? Will the rides and attractions be open??

Often the Schilthornbahn closes for maintenance in the spring. The Jungfraujochbahn should run year round, but check the website to see if there are any closures when you plan to be there.
http://www.jungfrau.ch/en/quick-navigation/top-of-europe/timetable/

I would recommend Wengen, if you want a mountain village, since it is served year round by the railway. Also, per my previous post, if you find good morning weather, you can get to the Jungfraujoch fairly quickly, as Interlaken is about 45 minutes further away.

When people use the term "cable car rides" and "attractions" it sounds as if you've got the wrong idea. The cable cars aren't used for joy-rides or sight-seeing. They're actually modes of transportation that the residents and tourists alike use to get from point A to point B. If they were just "attractions" or "rides" then they might close down when tourists season slumps, but they actually serve a purpose in being a part of the integrated Swiss Transportation System.

Yes April/May is a slow season with fewer tourists. But the alpine villages don't close down and turn off all the lights because there are people who actually do LIVE there and WORK there and FARM there and raise FAMILIES. So just to be clear, the alpine villages are not an amusement park full of rides and attractions. These are the Swiss Alps with spectacular natural scenery...open year round in some fashion.

I would recommend staying in Lauterbrunnen. It's not up high like Muerren and Wengen, but it is in a beautiful valley and at that time of year would be a safe choice: more quaint than Interlaken but less dicey than the mountain towns. You can easily get to Muerren and Wengen from Lauterbrunnen, as well as to the Jungfraujoch and Schilthorn, weather permitting. Hiking will depend on a lot of factors, but you can always ride the train to Kleine Schiedegg and on to Grindelwald as well.

Original post.

We enjoyed taking the boat across the lake to Weggis and Vitznau, then jumping on the Rigibahn to the top. Great views and a great boat ride.

Ooops. That is out of Luzern of course.