Welcome to my Swiss Alps. Even though it is a veryshort time, you should have a good trip. You have picked some good places. Possibly, you will not be able to do all of those things, but you should be able to get to most of them.
I'll only answer part of your questions directly
<<"Please advice how to go to Jungfrau region from the airport, which hotel should we stay, what kind of things are we looking in Jungfrau region, and the cost to go up to top of Europe.
Is it enough time to go around Jungfrau region for just one day?">>
It is not enough time to go around the Jungfrau region for one week, let alone one day. However, there is one important feature of the region which makes a one day only trip a particularly bad choice. it is the weather. You go to see the high altitude sights...the Jungfrau. If it is cloudy at high altitude, you pay a lot of money to see the inside of a cloud. Boring and expensive, both at the same time. ;-(
The weather can change rapidly; forecasts around the mountains are not reliable for more than 24 or at most 48 hours, and there can be sudden changes. The best approach is to locate at Interlaken (not a good tourist destination but a good transport hub) and go somewhere else by train if the Jungfrau is socked in. If the weather is good, you can catch frequent trains to the Jungfrau.
Also, April is still pretty much late winter at high altitudes. The snow cover is getting bad for skiing, so there are not so many skiers, but it is heavy enough that the hiking trails are all closed above maybe 1500 or certainly 2000 meters. Some hotels and restaurants will be closed until June.
So, your opportunity to do some really nice hikes would not exist until late June or early July. For a comparison- the automobile roads that cross the high Alpine passes open in the first or second week of June when the snow can be plowed away and generally will stay away.. Generally, that is, unless there is a late snow.
Check these links:
How to get there? By train.
Look in the timetable:
Please be sure to read the introduction pages.
Enter Zurich Airport for your starting point. End at Interlaken or Wengen or Grindelwald. Depending on whether you come from a Schengen country ( no passport check) or instead from one that requires a passport check, you can be on a train as soon as one hour or 1 1/2 hours after you are out of the airplane.
See attached screen grab. Most of those trains connect at Zürich main station and Bern. Some go direct to Bern and have only one connection to continue to Interlaken....connecting at at Bern.
Click on the "+" to the left of any trip for more details.
If you buy a ticket at the ticket counter, they will print out an itinerary for you. Nice,but not necessary. Please note that there are frequent trains and your ticket or rail pass will be good on any of them for that day. So, if you miss one, catch the next one.
If a fare is shown in the timetable, it is usually a 50% fare for Swiss residents who have a 50% general discount card. Arno and Annika are experts on train costs and discount passes. I am not.
This will start you on the Jungfrau region:
Let us know your thought as you proceed with your plans. We can offer suggestions.