Oops, I missread traktos as tranoktos and wrote "I'll never spend the night with him!". Freŭda mislego. ^^
Without looking it up (but as a fluent speaker) I would say that "trakti" means that you're going to handle something or take care of something. The word "kun" here surprises me a little... and I would say that it would have to mean "I will never take on issues while working with him on those issues".
Yeah. I guess I need to look it up...
Yes, after reading in vortaro.net, I think that's more or less it.
Because it is not the direct object of the verb. There is a preposition, kun, and prepositions only take -n when they denote direction.