Um, I get the vague gist about what your asking. I think tp is not quite up to discussing it's own syntax, so I'll keep answering in English.
kepeken - instrumental. mi moli e jan ike kepeken palisa pi kiwen suno. I killed the enemy with a sword.
poka - definitely collaboration, maybe geographic position without lon.
mi moli e jan ike poka jan pona mi. I, in collaboration with my friend, killed the enemy.
? mi moli e jan ike poka jan pona mi. I killed the enemy (that happened to be standing next to my friend).
lon - best to use this just for geographic location and not metaphorical uses since the metaphors aren't part of the language's specification.
lon sike, lon anpa, lon sewi = physically around, under, above.
lon poka - I don't know if this is a better way to say, 'physically next to" poka is a preposition officially so it can stand alone and people do sometimes use it for physically next to, but I feel like it would be more regular to say "lon poka" (or maybe it would be more regular to just turn sike, anpa, sewi into spatial prepositions already)
sama - works the same as predicative sentences-
waso li waso pi tawa noka. The bird is an ostrich.
waso li sama waso pi tawa noka. The bird is similar to an ostrich.
tawa - purpose and physical motion towards, dative.
tan - explanatory cause of
And for some reason, most people front this.
tan jan lawa la mi pakala ala e lawa. Because of the king, I don't break the laws.
mi pakala ala e lawa tan jan lawa. Seem valid and seems like the same thing, but everyone seems to want to front the prepositional phrase.
e- accusative, Direct object.
Advance toki pona
Unmarked complements. Starting with "jan li kama sona" or "jan li tawa tomo" as a model, you could argue that these are verbs without marked complements, or "jan li toki sona" I try to avoid these unless I feel like pressing the boundaries of the language because there just isn't a lot of support in the canon and what unmarked complements we have could be analyzed in other ways- adverbs, modal + verb, etc.
Applicatives. Some languages will promote an oblique (e.g dative to accusative) to show that the oblique thing is more topically important.
The syntax of toki pona is rigorously defined. How to translate the syntax into meaning isn't so rigorously defined, that's why I'm calling those two scenarios "advanced"