Questions About AST Validation

I’m writing a transpiler and came accross the topic of validating the input. I have some questions, but would also like to double-check if I understood everything correctly. To my understanding, there are 3 main validations you have to do when transpiling (or compiling) a programming language:

  1. Syntax/grammar validation. This is done in my case by ANTLR which makes sure the input respects the BNF grammar.

  2. Context validation. ANTLR only makes sure the input respects the grammar, but the grammar is context-free: for example the grammar of Java allows public, private, protected access modifiers on a class, but it will allow a class to have all 3 of them, it doesn’t know that a class should only have one of them. So this second validation makes sure that, for example, a class does not have more than one access modifier - I imagine I can do this as a visitor pattern on my AST, right?

  3. Dependencies/references validation. Check that we have for example all the classes which are declared as import statements in the current compilation unit - this also seems fairly easy, but what do you do about method references/calls to 3rd party classes? Say, for example, your code calls a class from JDK – how do you check that a reference to that class is correct, do you need to also compile that class and add it to your AST?

For example, you can use java.util.List in Kotlin. How does the Kotlin compiler know to tell you if you are using a String instead of an Integer when calling List.get(int index)? Does the Kotlin compiler also compile the java.util.List interface?

Thank you for reading, any response is appreciated.