For questions 1 and 2, the key thing you need to learn about is generics.
If you write
ArrayList dates = new ArrayList();
then you get a raw type: the compiler doesn't know what sort of thing you can put into your ArrayList. But when you write
ArrayList<Date> dates = new ArrayList<Date>();
then the compiler knows that this ArrayList will store instances of Date, and it can do some checking that you're only trying to insert and retrieve Date values. This is there both to protect and to avoid unnecessary gymnastics. With this second one, you will find that
dates.add(new String());
won't compile because the compiler knows that you're trying to put something of the wrong type into the list. Similarly, you can just write
Date date = dates.get(0);
because the compiler knows that what's inside will be a Date. With your first form, that wouldn't be the case: the compiler can't enforce any type checking, and so you would need to cast it when you got it out:
Date date = (Date) dates.get(0);
Using raw types can lead to errors in your program where you put the wrong type in by accident and the compiler won't be able to stop you; and it also makes it unnecessarily verbose when you retrieve things because you have to do the casting yourself. Think of the generic type parameter (the <Date> part) as being a way of enforcing what can go into, and come out of, the list. (Technically, this is only enforced by the compiler, and not by the runtime, but that's a lesson for another day... look up type erasure if you're interested.)
For this code:
Person p = new Student();
Student s = new Person();
List<Person> lp = new ArrayList<Student>();
List<Student> ls = new ArrayList<Person>();
you hit one of the most annoying aspects of the type system. Although Student is a subtype of Person, that doesn't mean that ArrayList<Student> is a subtype of ArrayList<Person>. It would be nice if it were so, but it's not. So:
Person p = new Student();
This line above is fine. A Student is a Person, so a Person reference can hold a Student instance.
Student s = new Person();
You can't do this line above, though. The reference s has to hold a reference to a Student; and a Person is not necessarily a Student. This will give you a compile-time error.
List<Person> lp = new ArrayList<Student>();
It would be nice if this one worked, but it doesn't. If you want an ArrayList<Student> then you have to have List<Student> as the formal type of lp.
List<Student> ls = new ArrayList<Person>();
This wouldn't work under any circumstances, for the same reason that the second line failed: a Person isn't necessarily a Student, and the List<Student> can't be expected to hold anything that isn't a Student.