[Asus Transformer TF700] wnerw:
So here goes some more ls -l...

root@tf700t:/ # ls -l storage
d---r-x--- root sdcard_r 2014-04-17 23:10 emulated
lrwxrwxrwx root root 2014-04-17 23:08 sdcard0 -> /storage/emulated/legacy
drwxrwx--x root sdcard_r 1970-01-01 01:00 sdcard1
drwx------ root root 2014-04-17 23:08 sdcard2
drwxrwx--x root sdcard_r 2014-04-17 23:08 sdcardi
drwx------ root root 2014-04-17 23:08 usbdisk0
drwx------ root root 2014-04-17 23:08 usbdisk1
root@tf700t:/ # ls -l datai
drwx------ root root 2014-04-17 08:59 Folder
drwxrwx--- root root 2014-04-17 23:08 media
root@tf700t:/ # ls -l datai/media
drwxrwxrwx root root 2014-04-18 00:46 0
drwxrwxrwx root root 2014-04-05 17:31 TWRP

Note that 0 is created by me, I changed its permissions after it gave no solution. I also created a file under 0, but it doesn't appear under sdcardi. I'm getting sleepy and confused, it's 1 am here... I really apreciate your help guys. I'm eager to keep solving this.

EDIT I have no idea which of my actions did this, but /dev/fuse for storage/sdcardi changed to rw, here:

rootfs / rootfs ro,relatime 0 0
proc /proc proc rw,relatime 0 0
sysfs /sys sysfs rw,relatime 0 0
debugfs /sys/kernel/debug debugfs rw,relatime 0 0
none /sys/fs/cgroup tmpfs rw,relatime,mode=750,gid=1000 0 0
tmpfs /dev tmpfs rw,nosuid,relatime,mode=755 0 0
devpts /dev/pts devpts rw,relatime,mode=600 0 0
none /dev/cpuctl cgroup rw,relatime,cpu 0 0
none /acct cgroup rw,relatime,cpuacct 0 0
tmpfs /mnt/asec tmpfs rw,relatime,mode=755,gid=1000 0 0
/dev/block/dm-0 /mnt/asec/se.feomedia.quizkampen.pl.premium-1 ext4 ro,dirsync,nosuid,nodev,noatime,user_xattr,acl,barrier=1 0 0
/dev/block/dm-1 /mnt/asec/de.tsorn.FullScreenPlus-1 ext4 ro,dirsync,nosuid,nodev,noatime,user_xattr,acl,barrier=1 0 0
tmpfs /mnt/obb tmpfs rw,relatime,mode=755,gid=1000 0 0
tmpfs /mnt/fuse tmpfs rw,relatime,mode=775,gid=1000 0 0
/dev/block/mmcblk0p1 /system ext4 ro,relatime,user_xattr,acl,barrier=0,data=writeback,noauto_da_alloc 0 0
/dev/block/mmcblk0p2 /cache ext4 rw,nosuid,nodev,noatime,nodiratime,errors=panic,user_xattr,acl,barrier=0,noauto_da_alloc,discard 0 0
/dev/block/mmcblk1p2 /data f2fs rw,relatime,background_gc=on,discard,user_xattr,acl,errors=panic,active_logs=6 0 0
com.android.browser_cache /data/data/com.android.browser/cache tmpfs rw,relatime,size=102400k 0 0
mobi.mgeek.TunnyBrowser_cache /data/data/mobi.mgeek.TunnyBrowser/cache tmpfs rw,relatime,size=102400k 0 0
/dev/block/mmcblk0p8 /datai ext4 rw,nosuid,nodev,noatime,nodiratime,errors=panic,user_xattr,acl,barrier=0,data=writeback,noauto_da_alloc,discard 0 0
/dev/fuse /mnt/shell/emulated fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
/dev/fuse /storage/sdcardi fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
tmpfs /storage/emulated tmpfs rw,nosuid,nodev,relatime,mode=050,gid=1028 0 0
/dev/block/vold/179:49 /mnt/media_rw/sdcard1 vfat rw,dirsync,nosuid,nodev,noexec,relatime,uid=1023,gid=1023,fmask=0007,dmask=0007,allow_utime=0020,codepage=cp437,iocharset=iso8859-1,shortname=mixed,utf8,errors=remount-ro 0 0
/dev/fuse /storage/sdcard1 fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
/dev/fuse /storage/emulated/0 fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
/dev/fuse /storage/emulated/0/Android/obb fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
/dev/fuse /storage/emulated/legacy fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0
/dev/fuse /storage/emulated/legacy/Android/obb fuse rw,nosuid,nodev,relatime,user_id=1023,group_id=1023,default_permissions,allow_other 0 0

But the problem still persists, I can't write to sdcardi.