You (the OP) seem preoccupied with OO design, well, I'll put it this way when thinking about the static variables things. The core concept is encapsulation and reuse; somethings you could care less about reusing but you almost always want the encapsulation. If it's a static variable, it's not really encapsulated, is it? Think about who needs to access it, why, and how far you can HIDE it from client code. Good designs often can change their internals without much breakage to clients, that is what you want to think about. I agree with Scott Meyers (Effective C++) about many things. OOP goes way beyond the class keyword. If you've never heard of it it, look up properties: yes they can be static, and C# has a very good way of using them. As opposed to literally using a static variable. Like I hinted at the start of this list item: think about how not to shoot yourself in the foot later as the class changes with time, that's something many programmers fail to do when designing classes.
Take a look at that Rx framework someone mentioned. The threading model to use, for such a situation as you described, is not readily decidable without more specifics about the use case IMHO. Be sure you know what you're doing with threads. A lot of people can't figure out threads to save their lives; it's no that hard, being tread safe can be when (re)using code. Remember controllers should often be separate from the objects they are controlling (E.g. not the same class); if you don't know it, look up a book on MVC and buy gang of four.
Depends on what you need. For many applications a class that is almost entirely filled with static data, is good enough; like a singleton for free. It can be done very OO. Sometimes you would rather have multiple instances or play with injection, that makes it more complex.
I suggest threads and events. The ease of making code event driven is actually one of the nicer things about C# IMHO.
Hmm, killing off singletons...
In my experience, a lot of the more common uses that young programmers put singletons to, are little more than a waste of the class keyword. Namely something they meant as a stateful module being rolled into a highlander class; and there are some bad singleton implementations out there to match. Whether this is because they failed to learn what they're doing, or only had Java in college, I dunno. Back in C land, it's called a using data at file scope and exposing an API. In C# (and Java) you're kind of bound to it being a class more than many languages. OOP != class keyword; learn the lhs well.
A decently written class can use static data to effectively implement a singleton, and make the compiler do the leg work of keeping it one, or as one as you are ever going to get of anything. Do NOT replace singletons with inheritance unless you seriously know what the heck you are doing. Poorly done inheritance of such things, leads to more brittle code that knows waaaay to much. Classes should be dumb, data is smart. That sounds stupid unless you look at the statement deeply. Using inheritance IMHO for such a thing, is generally a bad thing(tm), languages have the concept of modules/packages for a reason.
If you are up for it, hey you did convert it to singletons ages ago right? Sit down and think a bit: how can I best structure this app, in order to make it work XXX way, then think how doing it XXX way impacts things, for example is doing this one way going to be a source of contention among threads? You can go over a lot of things in an hour like that. When you get older, you'll learn better techniques.
Here is one suggestion for an XXX way to start with: (visualize) write(^Hing) a composite controller class, that works as a manager over the objects it references. Those objects were your singletons, not the the controller holds them, and they are but instances of those classes. This isn't the best design for a lot of applications (particularly can be an issue in heavily threaded ones IMHO), but it will generally solve what causes most younglings to reach for a singleton, and it will perform suitably for a vast array of programs. It's uh, like design pattern CS 102. Forget the singleton you learned in CS 607.
That controlling class, perhaps "Application' would be a more apt ;), basically solves your need for singletons and for storing configuration. How to do it in a sublimely OO way (assuming you do understand OOP) and not shoot yourself in the foot (again), is an exercise for your own education.
If it shows, I am not a fan of the so called singleton pattern, particularly how it is often misused. Moving a code base away from it, often depends on how much refactoring you are prepared to use. Singletons are like global variables: convenient but not butter. Hmm, I think I'll put that in my quotations file, has a nice phrase to it...
Honestly, you know more about the code base and the application in question then anyone here. So no one can really design it for you, and advice speaks less then action, at least where I come from.