Are there any religions like Christianity & Atheism among the people of Middle-Earth?

I don't think so....The existence of Iluvatar and the Valar, Ainur, and Maia, (who are rather god-like since they created Middle-Earth and its inhabitants), is more of a fact that everyone accepts than a religion that only some people believe in.

I think not. But I am sure that people of M.E. beleve in good and bad forces. Just like Gandalf said in FOTR: "So do all who live to see such times, but that is not for them to decide. All we have to decide is what to do with the time we are given. There are other forces at work in the world than the will of evil."

Middle-Earth is a monotheist world (not pagan!) before coming of Christ. There are strong structural parallels between Eru and God the Creator, the Valar and Maiar and angelic powers (or "gods" in Plato's Timaios dialogue, which are not the same as the Creator - they can form the world only according to His design), Melkor and Lucifer, fall of Numenor and the Deluge (but you can't tell that these parallels are direct analogies with Christianity or allegories, since you can find such parallels in other myths too, not only in the Bible). It's like the Old Testament, but in perception of other culture than judaic-christian, therefore differences in details. Tolkien's hierarchic image of the world and his presentation of Good and Evil (the Evil is not substantial at last) reminds the (neo)platonic one, it is especially clearly seen in Ainulindale, the first part of the Silmarillion.

In The Lord of the Rings there are not so many mentions of these things, but for example Denethor's and Gandalf's contraposition of -heathen- kings of old and their contemporary situation is not without purpose (it implicates that their world is alredy not heathen). On the other hand, it looks like these beliefs are not very institutionalized (there are no temples and priests mentioned), so you can't call them a real religion.

In general, it seems to me very interesting how Tolkien showed us how many structures are common for different myths and how many bounds connect us (christians or post-christians) with the people of old actually (and that many old cultures were much more than primitive pagans).

I think more like pagan religion.But the battle between good and evil would suggest christian.I guess it's how you want to see it.

Yes Christianity. How? Sauron is thought of as Luicfer and Gandalf as God. I think that's how my Youth Pastors wife explained it to me.