Translation:We go with them to do what they want.
Interesting - your "tion, kion" structure sounds like a translation from Russian, and I'm glad to see the moderator (amazulo) said it was acceptable. Zamenhof apparently wanted to leave some leeway in Esperanto for just this reason. A simpler example is the freedom to place an adjective after the noun (although I know the standard location is before the noun).
The beginning section is "We go with them" The "with them" is not the recipient of the action of "going", instead, it's a prepositional clause describing the going.
In general, anything noun after a preposition (with, to, over, etc.) is going to be apart of the prepositional phrase and, thus, not accusative. :)
"Fari" and "farti" are different verbs.
"Fari" is "to do/make", like "hacer" in Spanish.
Only use "farti" if you could use "fare" in English (forget the quaintness and focus on the meaning):
Kiel vi fartas? - How are you? (How do you fare?) Mi fartas bone, dankon. - I'm well, thanks. (I fare well, thank you.)