Tails has an option for opening existing Veracrypt Volumes, but can I create such volumes on Tails, and if so how? or do I need to create an admin password and install VeraCrypt?
Yes, you need to install Veracrypt first. Then create the drive. But once it's created you never need to install Veracrypt again, just open it from the embedded Tails software.
Also note that only Serpent, Twofish, and AES can be read with the Tails software. The other algorithms don't work, such as Camellia. And they only work individually, so don't try stacking them...for example AES(Twofish(Serpent)) won't work.