Triple Booting Mac, Windows, and Linux—A boot load nightmare

As for your first question:

As you probably have already read from the rEFInd web site, the commands. to make rEFInd appear at startup are given below. You would have to enter these commands after booting to the macOS 10.13.2 recovery partition. You could enter the commands while booted to macOS 10.13.2, but you first would have to disable System Integrity Protection.

diskutil  mount  disk0s1
sudo  bless  --mount  /Volumes/EFI  --setBoot  --file  /Volumes/EFI/EFI/refind/refind_x64.efi  --shortform
diskutil  unmount  disk0s1

If the above does not work, then rEFInd is not installed as you described in your question.

As for your second question:

I an not sure why you are worried if the disk utility can recognize your linux partition. Unless you have installed some third party software, macOS can not read linux formatted partitions. Your question gives no indication that you have install such software. Anyway, the output from the diskutil list command shows that the linux partition is being correctly recognized.

If the files on the linux partition are important, then I would think the first priority would be to remove the files from the internal disk. This could be done by creating a a Ubuntu bootable flash drive and boot to a Live version of Ubuntu. If you can access your files, then I would copy the files to a second backup flash drive or other external drive.

Just to let you know:

If you do decide to start over, I would suggest installing the operating systems in the following order.

1. Install macOS
2. Use the Boot Camp Assistant to install Windows.
3. Install Ubuntu using the instructions given here.
4. (Optional) Install rEFInd.