1.1.4 (the "ä" update) broke phone. Fix? Backup remotely?

SSH is asking for a password everywhere! You can set that in Settings -> Developer Mode. You have some options now, depending on your state you may setup that password and become root on the device eg open terminal devel-su and do a manual upgrade pkcon refresh and then version --dup, it will either run through and install some missing dependencies or it will cry out loud, see journal or dmesg and terminal output for error messages that might tell you what to remove or what has an issue (you can come back with that info here or better join IRC freenode #jollamobile for help), if you are already far away from that so you only have recovery-mode left as final option, there you could mount the home subvolume and your uSD to save to...

Im using Terminal app on Jolla. devel -su gives:

devel: command not found

pkcon refresh gives:

Refreshing cache
Waiting in queue
Waiting for authentication
Waiting in queue
Starting
Fatal error: Rpm Exception

Repeating pkcon refresh gives:

Refreshing cache       [       ] (0%) The deamon crashed mid-transaction!

version --dup gives:

REFRESHING CACHE
[W]QDBusConnectionPrivate::serviceOwnerChangedNoLock:1280 - QDBusConnection: name 'org.freedesktop.PackageKit' had owner '' but we thought it was ':1.2476'
Preparing
Error: Rpm Exception
Finished transaction (status=2, runtime=0ms)
UPGRADE NOT COMPLETE - Retry 1 of 3
Waiting 1 seconds before retry.
REFRESHING CACHE
Finished transaction (status=2, runtime=0ms)
UPGRADE NOT COMPLETE - Retry 2 of 3
Waiting 3 seconds before retry.
REFRESHING CACHE
Finished transaction (status=2, runtime=0ms)
UPGRADE NOT COMPLETE - Retry 3 of 3
Waiting 5 seconds before retry.
REFRESHING CACHE
[W] PackageKit::Transaction::parseError:803 - Transaction::parseError: unknown error "'org.freedesktop.DBus.Error.NoReply"' 
Finished transaction (status=2, runtime=0ms)
FINISHING

The upgrade could NOT be finished. Make sure you have a working Internet Connection and SSU is properly set up. In
case the repos are changing rapidly (e.g. during development),
just restarting the upgrade might fix the issue.

REBOOT AT YOUR OWN RISK

"see journal or dmesg" - I don't know what that means.

it is devel-su not devel -su - first of all, if you are not familiar with the command prompt, how about NOT just doing all things one after another when the first command returns an error already? Something in your setup is not working, it can be a broken Jolla Account, ssu isn't setup correctly and so on...Are you able to install apps from store?

Well, you said you wanted to see "output for error messages that might tell you what to remove or what has an issue (you can come back with that info here" In that case, I'd assume I should collect all the errors and not stop "when the first command returns an error already". Sorry if I misunderstood.

Store launched at first and I tried to install a random Sailfish app. It gave me the little "Waiting" note in the app listing, then "Store is not responding. Wait / Close". I waited and it eventually crashed. Now, when I try to open Store again, I see this:

When I go to Settings|Accounts, either Settings app crashes as soon as I tap on "Accounts" or it opens,I try to re-login to my Jolla account and get:

BTW, trying to get to the developer mode panel in Settings just shows these marching light dots forever:

On the upside, I finally remembered my dev mode password. So here is the output when executed in root. Stopping after the first error:

Could it be that your internal storage is full? It sounds like either your filesystem is not writable or your accounts got shredded. I have no clue about recovering accounts (lookling into it now), btrfs recovery on the other hand is try to delete some bigger files then balance btrfs. If you are unable to delete files you may try to ZERO them with true > $path_to_file then reboot and try to delete them again, after that, balance (might take a while). Balancing is btrfs balance start /