For example, if an NPC escalates conflict to gunfight, but my PC does not want to shoot him and tries to resolve situation by just talking while evading shots - can he not escalate and not roll dice for acuity+will, and consequently, still inflict talking fallout instead of gunfight fallout to NPC?
Yes, a character in Dogs in the Vineyard can choose not to escalate at the same time as an NPC. PCs don't escalate until they do something escalate-y.
In addition, fallout dice are determined by the action being done, not the current escalation level. If you've escalated to shooting, but you're trying to talk someone down this turn, you only inflict talking fallout.