Weird folder setup in Big Sur compared to Mojave. Lots of questions

I just upgraded to Big Sur from Mojave. Why are there 3 Applications folders in Big Sur?

1. One listed on main hard drive which seems to contain everything
2. Another in system folder: only some programs here. These are also in main folder
3. For the third go to System/Volumes/(hard drive name)/ all apps in this folder.

In this same folder I see the all the folders and files from my previous Mojave system. Should they be there? What do I do with them? Weird place to store files.

Everything is correct. This is all due to the split of the system volume (Macintosh HD or whatever you called it) into a read-only volume and a read-write volume.

Start by looking at the disk with Disk Utility. Press Command-2 (or tick Menu -> View -> Show All Devices). You should see something like this (the names will be different):

Within the APFS container you can see two volumes. In myself case BethSSD and BethSSD - Data. In what follows replace these with your own system volume name.

BethSSD is the read-only (highly protected) volume created by the macOS install and has the same content same on every Mac with the same version of macOS.

BethSSD - Data is a read-write volume and contains everything not part of the read-only volume. As well as your files, it includes all the application you have installed.

So we have two volumes and both will have applications - so Finder does some trickery to show them as one.

Taking your three locations (but in a different order) and a fourth:

2 The applications on the read-only volume are the Apple macOS applications and can be seen in /System/Applications.

4 (what you have not seen): In Terminal do ls /System/Volumes/Data/Applications. Here you will see all the applications you have installed - but none of the inbuilt macOS apps.

1 and 3. macOS combines the two locations above into one using "firmlinks". These are what you are seeing as/System/Volumes/<name>/Applications as well as /Applications.

I hope that helps. To go much further requires much mind bending!