Is there a way to make Windows Fastboot and Ubuntu work together?

Short answer:

No.

Long answer:

The "Fast Startup" name is something of a misnomer. This Windows feature actually turns shutdown operations into hibernation (suspend-to-disk) operations. As such, filesystem data structures are left in an inconsistent state. When another OS, such as Ubuntu, boots, it sees the disk in an inconsistent state, assumes that the previously-running OS crashed, and will either attempt to repair the disk or refuse to mount it. Thus, the Windows "Fast Startup" feature is fundamentally incompatible with a dual-boot setup. In principle, it could be fixed by having Windows sync its disks before doing its suspend-to-disk operation, but this would require changes in Windows, or at least a new third-party utility to add the functionality. I don't know how practical such a change would be, and AFAIK no such feature or add-on tool is available.

As a side note, the Windows "Fast Startup" feature is entirely different from the firmware feature that's often called "fast boot" or "fast start." This firmware feature takes shortcuts on hardware initialization in order to speed up the boot process. For instance, the firmware's fast start might skip initialization of some or all USB devices. This firmware feature usually works fine with Ubuntu, with the caveat that it may be impossible to boot an Ubuntu installer because the firmware won't see the USB flash drive. If you can boot acceptably, though, you can leave the firmware "fast start" feature active.

Yes. There is a workaround for that.

Windows "Fast Startup" is just hibernation. That's why Windows partitions can not be mounted with read-write permissions.

But if you setup /etc/fstab that Windows partitions are mount as read-only, you will "see" them. But you will be unable to write there.

It may be acceptable or not. But it is the only way to use Ubuntu with Windows "Fastboot" enabled.

If more detailed explanation on 'fstab' is needed, you can find it here.