Scala abstract class instance

Regarding:

val myList = List(1,2,3)

When the compiler encounters an expression which creates a class instance without the new modifier, it looks up that classes companion object to look for a .apply method. In the case of list, it is defined as:

override def apply[A](xs: A*): List[A] = xs.toList

Thus, this compiles successfully. You can view this when asking the compiler to emit type information after the typer phase:

def main(args: Array[String]): Unit = {
  val l: List[Int] = scala.collection.immutable.List.apply[Int](1, 2, 3);
  ()
}

Would myList be a reference to the List object isntance?

The run-time type of myList would be either a cons (::) or the empty list (Nil).

if productElement is an abstract method how can that be implemented?

This is a compiler trick. productElement and productArity (and more) are both generated at compile time for any case class definition. For example, given the following case class:

case class Bar(i: Int)

The compiler generates:

// an incomplete view of the generated case class methods and fields
// omitted for brevity.
case class Bar extends AnyRef with Product with Serializable {
  <caseaccessor> <paramaccessor> private[this] val i: Int = _;
  <stable> <caseaccessor> <accessor> <paramaccessor> def i: Int = Bar.this.i;
  def <init>(i: Int): yuval.tests.Foo.Bar = {
    Bar.super.<init>();
    ()
  };
  <synthetic> def copy(i: Int = i): yuval.tests.Foo.Bar = new Bar(i);
  <synthetic> def copy$default$1: Int = Bar.this.i;
  override <synthetic> def productPrefix: String = "Bar";

  // this is the relevant part to your question
  <synthetic> def productArity: Int = 1;
  <synthetic> def productElement(x$1: Int): Any = x$1 match {
    case 0 => Bar.this.i
    case _ => throw new IndexOutOfBoundsException(x$1.toString())
  };