How to Cut folders/files/photos and paste them to e.g. differrent folder. cmd x does not work.

There is no such feature, and for good reason. Suppose you cut a file, and the machine crashes before you can paste it. What then?

As Linc says, that is not something you can do on a Mac. It's possible to do cut safely with files, but in order to do so, you have to make it work differently than with text, which is confusing and inconsistent. Apple does not like unsafe or inconsistent, so they have not added such a feature.

Note that you can just drag files from one place to another to move them. (For safety, this copies when moving from one disk to another, but you can force it to move instead of copy by holding down the command key when you drop the file(s) on the destination. This is not necessary when moving from one place to another on the same disk.)

You can delete a file or folder via a keyboard command. Select the file or folder by clicking on it once, then press Command-Delete. This will move the item into the Trash.

You can also empty the Trash via a keyboard instruction - Command-Shift-Delete