I can figure out most things that I need on music bee, but this is really not easy for us non techy people. Think that's why you get these kinds of questions asked so often.
Thing is, it's a "techy" process.
So the questions are, how do I get the playlists recognised here, and then, how do I get the playlists to recognise the tracks on the portable drive instead of the c drive? (The file>advanced>remap command suggested on one post isn't available here.)
It's File->Library->Relink Music File Paths. You need to do things exactly as they are advised if it's going to work.
If you need help, you need to explain what you're doing and what you've already in a clear fashion. "On computer one I...then I...then on computer two I installed Musicbee portable and..."
Here's what I would do.
On Computer 1, if it's supported in your old, old version, export your layout View->Import Export->Export Panel Arrangement and save it somewhere on your computer
On Computer 1, if it's supported in your old, old version, export your settings Edit->Saved Settings->Save Settings Snapshot and save it somewhere on your computer
On Computer 1, File->Library->Open Library and make a mental note of where your library is located
On Computer 1, Install MB Portable
On Computer 1, In MB Portable, View->Import Export->Import Panel Arrangement and open the panel file you saved
On Computer 1, In MB Portable, Edit->Saved Settings->Load Settings Snapshot and open the settings snapshot you saved
On Computer 1, Close MB Portable
On Computer 1, Open MB Portable
On Computer 1, In MB Portable File->Library->Open Library and verify it's the same library as before or open it if it's not.
On Computer 1, Close MB Portable
On Computer 1, Copy the entire folder where MB Portable is installed to a thumb drive or something
On Computer 2, Paste the folder in the same location as it was on Computer 1
Move Your Music Library MBL File and your Music Files from Computer 1 to Computer 2, preferably in the same base drive/folder location as they were on Computer 1.
On Computer 2, Open MB Portable to verify it's laid out the way you expect
On Computer 2, File->Library->Open Library and open your library if it isn't already
If you couldn't move the music files to the same named base drive/folder location, File->Library->Relink Music File Paths and put the Computer 1 location on the left (like C:\Music for example) and the Computer 2 location at the right (like E:\Music or whatever). Just the part that has changed between the two installs.
Know that, because they are different computers, some settings may not work correctly on the new computer. Different fonts, etc. You will need to manage those things manually if that's the case. "Techy"
This is not a complete step by step guide. It's more like a list of signposts along the way. No two systems are alike. Things will come up along the way that you will need to figure out using logic and your experience using MB. When it's done, some things will likely not seem right and you will need to figure out how to fix them. This could probably get you most of the way there, though.
Good luck.