Facing problem while migrating API from mule 3 to mule 4

Several of the questions asked are already explained in the Migration Guide.

1. How to use the expression component in Mule 4?

In Mule 4 the expression language is DataWeave 2. You should learn about DataWeave and read the migration guide from MEL to DataWeave.

2. Are there any other ways to use session variables?

No. This is mentioned in the migration guide Migrating Core Components: "Session variables have been removed. Users must explicitly pass headers across transport boundaries."

3. In Mule 3, I used an expression component to return Java code to my logic. I'd like to reuse that Java code in Mule 4.

You can call Java static methods directly from DataWeave. Also you can execute any Java method with the Java Module and store the output in a variable to be used in a DataWeave script.

Additionally you can create custom functions to add to DataWeave using the Mule SDK.

Note that in Mule 4 you should not use any Mule APIs in your Java code.

Generally speaking try to see if you can use pure DataWeave features before trying to call Java code.

4. The message enricher component is not supported in Mule 4.

There is no need for the enricher. Mule 4 can use target variables in any operation. This is mentioned in the migration guide.

5. Mule 4 does not support transformers such as DOM to XML, XML to String, and so on.

That's right. You should use DataWeave Transformations instead of transformers. Yet another topic mentioned in the migration guide.