Hello,
when I move my userdata from my dietpi to an sd card which is mounted on
/mnt/f7525da9-f0b0-4110-8d8a-406722599a24/
and I do a dietpi backup to
/mnt/f7525da9-f0b0-4110-8d8a-406722599a24/dietpi-backup
is the userdata also included in the backup?
If it is in /boot/dietpi/.dietpi-backup_inc_exc then it will be included. The default is to exclude everything under /mnt but to include the /mnt/dietpi_userdata. Since you moved the userdata, verify that it is also changed.
Maybe, this blog post helps somehow to understand how to set the include paths correctly.
are you realy going to move your user data to a TF card? Personally, I would not do it that way. Usually people trying to move away from TF card to something like HDD/SDD or eMMC 
I am checking after my last fatal crash of my device what’s the best
When I have a dietpi backup on my external device and my device crashes and I reinstall dietpi but the uuids changed. Can I use the backup to install the same device as it was before but I need to change /etc/fstab and /boot/cmdline.txt
Correct?
Usually DietPi Backup will restore your entire system as it was before. And UUID should stay same if you don’t reformate the external drives.
But if I reformated the devices and the uuids changed
you mean for the boot device? Usually our backup tool should handle this
Very specific question, which I can try myself, but maybe someone knows 100%.
If I back-up my data, does it also backup my Chromium browser history?
Yes, it backups your complete system, also with all user data.
My system crashed ones and I had to complete recover my whole device with reflashing from scratch…see also Nano pi r5c not booting from EMmc anymore - #9 by temp
So also uuids changed how can I than recover the backup?
Simply restore your backup