How to create a recovery partition?
Is it possible to create a new recovery partition, and if so, how does
  it have to be done?


No, it is not possible...  later Sony devices use what is called "Recovery in Boot" and recovery resides inside the boot partition... Makes it much more difficult to install TWRP or other custom recovery or software because a custom boot image (kernel) is required.


  Or is it possible to flash a custom ROM without this partition?


Yes you can, in fact it is a requirement since stock software won't work with TWRP installed (the boot image fails validation, at least last time I looked), because there is a way to patch the boot partition and install TWRP.

So is the question how to install TWRP? No, that isn't really it either because with a locked bootloader you cannot. 

This is a journey you can take with help in a more relevant place... I already answered your questions as asked, but will give you some references to start reading about all the steps required.

Unlock bootloader

Official TWRP information

Install TWRP and FOTAkernel