[Xperia Z1 Compact General] Turbopuschel:
Ok, after I (think I) found out what logcat means and how to get it, this should be the relevant part. Here I first tried to format the /data partition as f2fs and after that (and the red error messages from TWRP) I tried to repair the filesystem. In the end (I think I cut off the log at that point, if I understand it correctly...?) I formatted again as ext4 and then restored /data from a nandroid backup.

If there is something relevant missing or I misunderstood something please tell me.

I:TWFunc::Set_Brightness: Setting brightness control to 255
I:operation_end - status=0
I:Set overlay: ''
I:Set page: 'clear_vars'
I:Set page: 'backup'
I:Set page: 'main'
I:Set page: 'clear_vars'
I:Set page: 'main2'
I:Set page: 'wipe'
I:Set page: 'advancedwipe'
I:checkpartitionlist list '/data;'
I:checkpartitionlist part_path '/data'
I:Set page: 'checkpartitionlist'
I:getpartitiondetails list '/data;'
I:getpartitiondetails part_path '/data'
I:Set page: 'partitionoptions'
I:Set page: 'selectfilesystem'
I:Set page: 'confirm_action'
I:Set page: 'action_page'
I:operation_start: 'Change File System'
I:sending message to remove 65537
mtppipe remove storage 65537
I:Message sent, remove storage ID: 65537
Formatting Data using mkfs.f2fs...

F2FS-tools: mkfs.f2fs Ver: 1.4.0 (2014-10-18) [modified by Motorola to reserve space]

Info: Debug level = 0
Info: Label =
Info: Segments per section = 1
Info: Sections per zone = 1
Info: Trim is disabled
Info: sector size = 512
Info: total sectors = 25178079 (12293 MB)
Info: zone aligned segment0 blkaddr: 512
Info: format version with
"Linux version 3.10.96-gdcd3ca1 (grapaul77@instance-3) (gcc version 4.8 (GCC) ) #1 SMP PREEMPT Tue Feb 16 21:32:22 UTC 2016"
Info: Overprovision ratio = 2%
Info: Overprovision segments = 227 (GC reserved = 108)
Info: format successful
I:mkfs.f2fs -t 0 /dev/block/mmcblk0p25 process ended with RC=0
Done.
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Unable to recreate /data/media folder.
I:Unable to mount '/data'
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Updating partition details...
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
I:Unable to mount '/usb-otg'
I:Actual block device: '', current file system: 'vfat'
...done
I:Set page: 'action_complete'
I:operation_end - status=0
I:Set page: 'clear_vars'
I:Set page: 'refreshfilesystem'
I:getpartitiondetails list '/data;'
I:getpartitiondetails part_path '/data'
I:Set page: 'selectfilesystem'
Truncating string cache entries.
I:Set page: 'partitionoptions'
I:Set page: 'advancedwipe'
I:Set page: 'wipe'
I:Set page: 'main'
I:Set page: 'clear_vars'
I:Set page: 'main2'
I:Set page: 'mount'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
I:Set page: 'main'
I:Set page: 'clear_vars'
I:Set page: 'main2'
I:Set page: 'wipe'
I:Set page: 'advancedwipe'
I:checkpartitionlist list '/data;'
I:checkpartitionlist part_path '/data'
I:Set page: 'checkpartitionlist'
I:getpartitiondetails list '/data;'
I:getpartitiondetails part_path '/data'
I:Set page: 'partitionoptions'
I:Set page: 'confirm_action'
I:Set page: 'action_page'
I:operation_start: 'Repair Partition'
Repairing data using fsck.f2fs...
I:Repair command: /sbin/fsck.f2fs /dev/block/mmcblk0p25
Info: sector size = 512
Info: total sectors = 25178079 (12293 MB)
Info: MKFS version
"Linux version 3.10.96-gdcd3ca1 (grapaul77@instance-3) (gcc version 4.8 (GCC) ) #1 SMP PREEMPT Tue Feb 16 21:32:22 UTC 2016"
Info: FSCK version
from "Linux version 3.10.96-gdcd3ca1 (grapaul77@instance-3) (gcc version 4.8 (GCC) ) #1 SMP PREEMPT Tue Feb 16 21:32:22 UTC 2016"
to "Linux version 3.10.96-gdcd3ca1 (grapaul77@instance-3) (gcc version 4.8 (GCC) ) #1 SMP PREEMPT Tue Feb 16 21:32:22 UTC 2016"
Info: superblock features = 0 :
Info: superblock encrypt level = 0, salt = 00000000000000000000000000000000
Info: total FS sectors = 25178072 (12293 MB)
Info: CKPT version = 1
Info: checkpoint state = 5 : compacted_summary unmount

[FSCK] Unreachable nat entries [Ok..] [0x0]
[FSCK] SIT valid block bitmap checking [Ok..]
[FSCK] Hard link checking for regular file [Ok..] [0x0]
[FSCK] valid_block_count matching with CP [Ok..] [0x2]
[FSCK] valid_node_count matcing with CP (de lookup) [Ok..] [0x1]
[FSCK] valid_node_count matcing with CP (nat lookup) [Ok..] [0x1]
[FSCK] valid_inode_count matched with CP [Ok..] [0x1]
[FSCK] free segment_count matched with CP [Ok..] [0x17cf]
[FSCK] next block offset is free [Ok..]
[FSCK] fixing SIT types
[FSCK] other corrupted bugs [Ok..]

Done.
I:/sbin/fsck.f2fs /dev/block/mmcblk0p25 process ended with RC=0
Done.
I:Set page: 'action_complete'
I:operation_end - status=0
I:Set page: 'clear_vars'
I:Set page: 'partitionoptions'
I:Set page: 'advancedwipe'
I:Set page: 'wipe'
I:Set page: 'main'
I:Set page: 'clear_vars'
I:Set page: 'main2'
I:Set page: 'mount'
Failed to mount '/data' (No such device)
I:Actual block device: '/dev/block/mmcblk0p25', current file system: 'f2fs'
I:Set page: 'main'
I:Set page: 'clear_vars'
I:Set page: 'main2'
I:Set page: 'wipe'
I:Set page: 'advancedwipe'
I:checkpartitionlist list '/data;'
I:checkpartitionlist part_path '/data'
I:Set page: 'checkpartitionlist'
I:getpartitiondetails list '/data;'
I:getpartitiondetails part_path '/data'
I:Set page: 'partitionoptions'
I:Set page: 'selectfilesystem'
I:Set page: 'confirm_action'
I:Set page: 'action_page'
I:operation_start: 'Change File System'
Formatting data using make_ext4fs...