How much free space should I leave on my Linode disk?

The resources that are listed in the Linode Manager are what you have available to allocate to your disks, based on what plan you choose for your Linode.

on my Linode (Linode 4GB: 2 CPU, 80GB Storage, 4GB RAM)… can I assign ALL of the space to my Ubuntu 16.04 LTS Disk?

In most cases, it is perfectly fine to use 100% of your allotment, as that will cover both your main disk and the swap image you create when deploying an image. If you've got additional needs for your storage, you'll likely have an idea of that prior to deploying your Linode. That will help you with determining how much of your storage you'll want to allocate to each disk.

Or is free space needed to accomodate swap files / backup functions?

A small swap image is typically created during the created during the creation of a new Linode, so you shouldn't need any additional swap space. Currently, when deploying a new Linode in the Cloud Manager, a 512 MB swap image is created automatically, along with your main disk. Together, those values should total 100% of your plans total storage.

I ma paying extra for Linode backups already, this doenst seem to figure in the disk space allocation as far as I can tell.

That is correct. Your Backups Service is independent of your Linode's storage, as all backups are stored in a separate location from your Linode's disks.

thanks! that seems clear then that I can allocate more to my LTS disk.

No problem! We've got a great guide that will walk you through resizing your disk.