1) It (I am answering this from the perspective of one religion, not all, and my own specifically) does not have a privileged position in the law of my nation. I think that it should ideally, although actually doing that is likely not prudent currently.
2) It does not have privilege socially all over but in some spots it probably does. I think that it should ideally but such if it occurs I doubt will last as the religion is meant to have enemies and be at enmity with the world, the flesh, and the demons.
3) I do so a lot and in a hierarchy and I think that I should do so. St. Paul said: "as we have opportunity, let us do good to all people, and especially to those who belong to the household of faith."
St. Thomas Aquinas expounds the point: "because we cannot do good to everyone, he presents the order in which it is to be done, when he adds: but especially to those who are of the household of the faith, who, namely, are not only akin to us in nature but united by faith and grace... Therefore mercy must be extended to everyone but preferably to the just who share in the faith, because it is said: but if any man does not have care of his own and especially those of his house, he has denied the faith and is worse than an infidel [quoting St. Paul again]."
Concerning my word "hierarchy," this means that for instance, if I were hiring for a job and all the candidates were otherwise equal except in religion I would select the Catholic first, then the Eastern Orthodox, then the Old Orthodox, then the Oriental Orthodox, then the Assyrian Orthodox (and divisions within them at random), then the Old Catholics... and so on, each religion being selected in order to it's proximity to my own, until something was intolerable.
This social privilege also applies to many other more practical things in my life, such as who I give deferrence to, those who I perceive to be theologically or philosophically (I add philosophy here for there are certain wise atheists who have absolutely no theological ability who I similarly give deferrence to) superior to me I do. Those wiser than me and with virtues I likewise do, and so on. This can include doing what they say when I ask them for advice, being more likely to spend time with them or aid them, etc. Just general social privilege.
I think I should do this especially to those who have fed me knowledge for "honor your father and your mother," in addition to all said above.
All the above is my opinion.