Running Mojave & Windows on Catalina

Well, the way I would do it is to start with two partitions of the size you would typically need for each OS. Install Mojave, first, on one of the partitions, and get it up and running. Next, I would install Catalina on the unused partition and set it up. Choose an emulator for windows. Below I have provided the several machine emulators that work on a Mac.

You will need the macOS full installers for Mojave and Catalina. I recommend you make bootable USB flash drive installers for each version of macOS: How to create a bootable installer for macOS.

1. Parallels Desktop for Mac. Parallels uses software virtualization to enable running Windows concurrently with OS X.
2. VM Fusion. VM Fusion is software virtualization that enables running Windows concurrently with OS X.
3. CrossOver. Enables running many Windows applications without having to install Windows. The Windows applications can run concurrently with OS X.
4. VirtualBox. Open Source freeware virtual machine such as VM Fusion and Parallels that was developed by Solaris. (Free because it comes with OS X. You must own a legitimate Windows Full Retail Installer.)
5. Wine. Allows OS X users to run Windows applications. Note: this is for the official release of Wine, which only provides source code. If you want a version of Wine that is packaged specifically for OS X, then use Winebottler, available here.
6. QEMU. A generic and open source machine emulator and virtualizer.

A license must be purchased for any commercial software and operating system products. Open Source software is free.

If you run Windows using Boot Camp, then you cannot add an additional partition for Mojave. However, if you run Windows in an emulator, like Parallels, then you can run Mojave on another partition along with Catalina. Or, switch it around and run Windows using Boot Camp, then run Mojave in the emulator.

No, I'm afraid one cannot do that because each OS must be booted from start in order to run. What you are asking could not be done because it would require a restart, selection of which OS to boot, then boot that OS. Nothing from one can pass to the other.

When you receive your new computer, you will find a very new learning curve with respect to both the hardware and macOS. New notebooks have the T2 chip that handles security. The computer will come with Secure Boot enabled. You will be blocked from partitioning and adding another OS unless you disable Secure Boot (About Secure Boot and System Integrity Protection for Macs.) Catalina now uses APFS disk formatting which supports both independent partitions or a form of disk space sharing called Containers. This reference may prove helpful: macOS User Guide.

For using Mojave there's always the option of installing it on an external hard drive, e.g. a USB SSD and then booting off that by changing the Startup Disk in System Preferences as and when needed. It would avoid you having to partition your existing Fusion drive.

Myself I went down the virtualization route and I regularly run multiple VMs using VMware Fusion (they are also planning to Support Big Sur when that finally ships). All my VMs are running on an iMac at the moment that is a Core i7 with 24GB of RAM and it works really well. Other benefits of a VM solution is that it saves time not having to reboot, you can test out software in Windows and Mojave while using Catalina for daily stuff at the same time, plus you can copy files between VMs if needed.

Yes, you can run such a VM in Parallels or one of the other emulators. The choice of emulator is difficult since each have pros and cons. Parallels is the ranking speed king. VMware Fusion provides the best protection against unwanted interactions between the emulator and macOS. VirtualBox, Wine, and QEMU are all free emulators. I do not know how well they compete against the top two for speed, ease of use, and compatibility with macOS. My personal choice for my own use has been Parallels.