The UI shows different colors based on value of status, but what role does resolution field play when editing a ticket?

The colors you see are simply those which were chosen when those ticket reports were created. It's likely that they were derived from existing reports in fossil's spiritual ancestor, CVSTrac.

The exact distinction between ticket status and resolution is not (IMO) 100% clear-cut and is largely a matter of taste. In principle, the status is generally a short list, possibly as short as (Open, Closed). The resolution, on the other hand, is intended to flavor that status with more detail, such as one of (fixed, will-not-fix, works-as-designed, ...).

The ticket system can be customized considerably, depending on a project's needs and/or its owners whims, and you could even remove the resolution altogether. See: src:/doc/trunk/www/custom_ticket.wiki and the /tktsetup page of a repo you are the administrator of.