For the most part, local rulers were all evicted by the Crusaders. There was no way any Muslim rulers were going to be left in places controlled by the Crusaders, they had all been forced to flee or killed en route. In the case of the local Christians things are a little more complicated.

The relationship between the Crusaders and the Armenian/Coptic Christians is something most general histories don't go into very much but is fascinating. The only Armenian controlled territory in Syria was Edessa which was taken over by Baldwin (future Baldwin I, the kinda/sorta first king of Jerusalem) during the course of the First Crusade. The short version is Baldwin got himself made heir to the county by the Armenian ruler and then a mob killed said ruler. Coincidence? Probably not. On a more local governmental level I'm not really sure if Armenian bureaucrats kept their jobs but I'd be willing to guess they did. The kingdom of Sicily, where many of the Normans on the Crusade came from and the only other state in Europe with a significant population diversity, used Muslims and Greek Christians as the backbone of their bureaucracy so it's likely that practice would be common in the Crusader States. Higher ranking Christians were generally removed from their positions. For example, the Patriarchs of Antioch and Jerusalem were promptly replaced with Catholic clergy depriving the Armenian church of much of its stature, although it was still allowed to practice in Crusader held lands.

They certainly wanted to convert the local populace and nobility but I don't know much about how successful they were. Fulcher of Chartres makes mention of converts near the end of his chronicle but it's in a section where he's trying to make Syria sound awesome to convince people to move there so he's not exactly at his most reliable.

The only case of intermarriage I can think of, although there may be some I'm not familiar with and I'm excluding cases where it was probably not voluntary (i.e. captive woman forced to marry), is the proposed but never executed marriage between Richard the Lionheart's sister and Saladin's brother. This was one of many stages in the peace talks between Richard and Saladin that took up a large portion of the Third Crusade. How sincere the parties were in this negotiation is pretty hotly debated by historians. In the end it didn't happen, at least one source claims Richard's sister refused to marry a muslim, so it's a bit of a moot point.

Anne-Marie Edde's excellent biography of Saladin (called simply Saladin) goes into pretty close detail on the more mundane matters of the Crusader States and near east Islamic territories. While she's obviously mostly focused on the mid-late 12th century she does give a lot of background as well.