"Achenar" comes from Arabic, so the sound is a voiceless uvular fricative. I'd render it as /'aXə,nar/ (I'm Scottish, so I pronounce post-vocalic Rs)
"Chnumar" I'd pronounce as /'xnu,mar/ with the same sound at the beginning.
"Archon" would be /'ar,kon/ for me, as it's clearly drawn from the pronunciation of "anarchy," which has a hard /k/ sound in modern English.
"Chona," for me, would have a standard English "ch" sound, probably because it's unusual for words in English to start with that digraph and not take the voiceless alveolar affricate sound as in "Charlie."
I'd pronounce it /'t͡sɔnə/.