I'm a sorcerer and have Tomi as henchman and I got the quest from a ranger elf or something in the core district by a big tree.

I'm supposed to rescue some animals from the zoo in the black-something district.

and to do that I'm supposed to cast a spell that I got from the ranger elf on a tree outside the zoo

but how do I cast it?

do I have to be a ranger, druid or cleric or something??

Enter the Zoo, when you open the door using the key you got from the Druid that gave you the quest there will be a long corridor that makes a left turn and ends in another door. This is marked on your map as "Exit to the big tree". Go out this door and you'll find a tree that highlights when you move your cursor over it, left click and the green letters will come up and include a statement which says "Cast teleport spell on tree". Pick that one and the tree will turn into a portal.