You're lucky! The internet means you can research anything you want. You're not limited to a few reference books in your local library or the memories of someone who might once have looked something up somewhere. Plus you're writing fantasy, so you're not constrained by the real world. So embrace your luck!
If you've never done any research before, then the easiest place to start is indeed Wikipedia. Just type in a word, find an article, read it, and let it lead you elsewhere, either to more articles on Wikipedia or to outside sources. At this point don't read with the intention of finding answers, just read to get background and ideas and general knowledge. If something strikes you as interesting, make a note of it, together with details of where you found the information, and then either copy and paste or take a screen shot of it, just in case the website fails or the Wikipedia page is changed. Keep different folders for different issues so you can find things easily when you need to. Not all of what you read will be accurate. Some things will be mistaken or phrased badly, some will be out-and-out lies or fantasy. Just roll with it for now. You'll only find out what is what by more reading and, the important bit, thinking about what you're reading.
Don't rely on the internet, though. Go to your library, see what's there. Browse through books about religion, perhaps, or lots of different places -- Bhutan, the Shetland Isles, North Korea, Cambodia, Polynesia, Cape Cod -- anywhere and everywhere.
But be careful. Some would-be writers love all this world-building stuff, and will take years working out different cultures and foodstuffs and wars and dress and, well, everything. Which is fine, but world-building is there simply to act as background to the story and the characters. In amongst all this anxiety about what nationality they should be and what weapons they should use, don't forget that this isn't important, the story is, and the characters are, and often you only know what the story is and who the characters are by writing them.
As to your specific questions:
Are there any male counterparts to a nun that I can research or that you know about?
There are monks in the major religions. There are also friars, who are members of mendicant orders, ie they go out into the world to preach and help, rather than staying in a closed monastery. There were/are also military orders such as the Knights Hospitaller which still exists as the Order of St John. Doubtless there are many other religious fraternities, but there's no reason you can't create your own -- this is a fantasy work, so you can extrapolate from the real world, you're not bound by it.
Are flagellants influenced of their beliefs by others that surround them or do they just act on choice without any influence?
"No man is an island, entire of itself; every man is a piece of the continent, a part of the main." So also, no one acts alone without any influence from other people, even if sometimes that influence is negative or the reverse of what is intended. So someone who is the child of an alcoholic might be a fervent tee-totaller; someone who is encouraged to be a doctor by his consultant parents might turn to banking. Find out who your characters are and who have influenced them for good or ill by thinking about them as real people not as puppets to be manipulated by you. Some writers "interview" their characters; some get the characters to write letters or their own biographies; some of us simply start writing and let the characters unfold as the plot happens.
Which places and/or parts of the world that exist today that realistically could easily be a place for dwellers to hide out which the outside society has the least chance of getting in the way of?
Well, where do you think might be hard to get to and from? Up a mountain, on an island, in the middle of a desert? But don't forget that small cults can exist in the middle of cities -- all it needs is a house, a domineering personality and people who are groomed/brainwashed/frightened to do anything to contradict what is said by the "master". Come to that, there are Christian cults which exert a lot of power over their members, stopping them from being fully in the society which surrounds them, and I see no reason to believe Christianity has a monopoly on them. So it's perfectly possible for a child to be born into a cult-like atmosphere and think it's normal to be beaten or whipped, and then to carry the physical and psychological scars of that childhood long after he/she has left the cult itself or the master has died/been imprisoned.
What kind of class or rank in a religious order setting would be victim to abuse, manipulation or being stirred into someones influential ways based on that leaders actions or what they preached to them?
Again, who do you think is going to be most easily a victim? The person at the top of the Order, or the lowliest member? A person with knowledge, power and self-confidence, or a person who is weak and powerless? Power corrupts those who wield it, but the powerful aren't usually themselves the abused, they're the abusers.
You've asked a lot of questions in your posts, but I think it's time you moved on from asking general questions of others, to asking questions of yourself. Only you know what interests you enough that you want to learn all you can about it. Only you know what excites you that you're keen to get started. Only you can write your story. So, let the adventure begin!
