You pronounce Onórach as "on-ore-uhk" except the "uhk" bit isn't a strong "hard k" sound ending, but a soft one. You know how the composer Bach is pronounced? well the -ach of Irish is similar to that. The accent on the second ó is a length mark to show the vowel has a long sound, not a short one.
In terms of what you want to say, well it's a bit hard sometimes to translate directly from Irish to English because we construct things differently in either language. Names are nouns rather than adjectives, so I'd probably go with Onór ("on-ore") rather than Onórach. You could use Onórach but then it would normally follow another noun such as Mac (son) or Fear (man) to express an honorable son or man, which is then followed by the lineage, but then your name title would be very cumbersome and lengthy.
As for the son of Arthur. It depends what you want to express by Arthur. ie. if you're wanting to use that name as in the British King Arthur, then yes use that form. If however you are using it in the sense of having a Bear ancestor (Art) then it would be MacAirt, the i in Art comes from the fact that names in Irish are given in the genetive case (possessive case) following the "son of" part.
Also we use the "mac" or "Mac" (sometimes shortened to Mc as a contraction of mac) differently in different eras. Let me see if I can remember this correctly:
If you are using a patronymic, ie. literally stating you are the direct son of Arthur, then you use a lower case mac. If using it as a surname such as a clan title from an eponymous ancestor, then upper case M - Mac. I think!
So "Onór macArthur "or "MacArthur" or "mac Airt" or "MacAirt" depending on what tribal/kin relationship and ancestor type you want to express.
Gets kind of complicated doesn't it?!
All the best!