What is the C# equivalent of NSMutableArray and NSArray?

That would be ArrayList and object[] respectively, if you take the weak typing nature of NSMutableArray and NSArray into account.

Arrays and lists in C# (at least for .NET 2.0 and above) can also be strongly-typed, so depending on what kind of object you're storing you can specify that type. For example if you only have NSString objects in an NSMutableArray in your Objective-C code, you'd use List<string>, and if you have them in an NSArray, you'd use string[] with a fixed size instead.

To quickly initialize and populate a list or an array in C#, you can use what's known as a collection initializer:

List<string> list = new List<string> { "foo", "bar", "baz" };
string[] array = { "foo", "bar", "baz" }; // Shortcut syntax for arrays

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string in C# is immutable, just like NSString in the Foundation framework. Every time you assign a new string to a variable, you simply point or refer the variable to a different object.

List<String> stringList = new List<String>();
stringList.Add("Test");

String in C# is immutable. The equivalent of NSMutableString in C# is StringBuilder. C#, unlike Objective-C doesn't represent the method intention clearly on the method name. For example, both classes String and StringBuilder has a method called Replace that you might think, replaces characters. String.Replace replaces and returns the new string whereas StringBuilder.Replace does a in-place replace.

Most methods in most classes in C# (and Java too) work like that.

In Obj-C, naming conventions are clear, it's either

[NSString stringByReplacing...]
[NSMutableString replace...]