It says under the demoralize rules that you can only threaten an opponent in this way if it is within 30ft and can clearly see and hear you. Thus we assume that demoralizing an opponent consists of verbal attacks and gestures.
If we treat Demoralize as verbal then it falls under the category of "Free Action - Speak", if you treat it as a gesture it would fall under the category of "Feint". Feint is considered a skill usage specifically designed for combat, just as Intimidate is.
No, you would not provoke an attack of opportunity from demoralizing your foe in combat.
That is because those skills are variations of things that normally DO provoke attacks of opportunity. Acrobatics/flying are variantions of moving. Moving normally provokes, so in these cases they dont. Drawing a weapon normally provokes, but with sleight of hand it doesnt.
Intimidate is a variation of talking more or less, which doesnt provoke. So unless the intimidate rules say it, it doesnt provoke.