A Roslyn analyzer can register a bunch of different code actions, eg. on the "whole file" level, the method, every single syntax node, or symbol. Depending on what you're exactly are trying to analyze, any of those might be applicable for you. Especially, as you indicate, you're concerned about performance. See the AnalysisContext.Register*Action() methods, for possible "hooks" you can add.

To get the things that you want:

1 Get the current class

Basically, with any of those, you should be able to get the current class (if registering syntax node or symbol action), or all declared classes (for example, with registering a compilation action, or syntax tree action). But the most simple option is to register a syntax node analysis for class nodes, you can do that like this:

context.RegisterSyntaxNodeAction(AnalyzeClassNode, SyntaxKind.ClassDeclaration);

Where AnalyzeClassNode is an action to analyze the class declaration. That will receive an additional context (a SyntaxNodeAnalysisContext), which contains the class declaration syntax node.

2 Get the namespace of the current class

For this, you need the semantic model. Let's say you used the RegisterSyntaxNodeAction method, and declared a method AnalyzeClassNode, then in the body, you can do this:

var classNode = context.Node;
var model = context.SemanticModel;
var classSymbol = model.GetDeclaredSymbol(classNode);

And you get the namespace symbol with:

var @namespace = classSymbol.ContainingNamespace;

And .MetadataName will give you the namespace as string.

3 Get all used types with their full name

That's something much more complex, and really depends on what you're trying to achieve here. To really get to something like "all dependent types, or imports". You should traverse the entire class node, get the symbol for every useful node (I have no idea what that would entail), and checking it's namespace, or full metadata name.

Maybe, you can elaborate a little bit more on this, to find out if this is the right approach.

By the way, check out "Learn Roslyn Now", a site with a bunch of tutorials for Roslyn. Specifically, you want to checkout part 3 (for syntax nodes), 7 (for symbols), and 10 (intro to analyzers).