Is it possible to mount APFS (Apple's newest file system) in Ubuntu 17.10?

No, and it probably won't be possible for a long while. From Apple's APFS FAQ:

Is APFS open source?

An open source implementation is not available at this time. Apple plans to document and publish the APFS volume format specification.

So after Apple releases the APFS specs (at some unspecified date), someone will have to do the implementation work, and it would probably take many years before it attains a decent level of functionality (especially if you want write access).

If you are willing to compile from source, you can try apfs-fuse from Github.

The author warns that it is in an early stage and read-only, but therefore shouldn't damage the disk you try to mount. To get just one or two files read from an Apple volume, it might be OK.