Java Date class- switches and ifs in the constructor
Getting your class compiling and working is an achievement in itself. So don't let my comments discourage you, but see them as hints for the next learning steps.

Processing time

Don't worry about that until you really experience performance problems. Even expert programmers often fail when trying to predict the performance of their code. If you run into performance issues, then learn to use analysis tools like "profilers". But most probably, you won't need them for the next few years.

Code in constructor

It's good to do validity checks in constructors. But you're right, the constructor's readability suffers from its length. The key to readability is introducing good abstractions instead of writing lengthy code, as you already did with the leap() method. Writing a monthLength(int year, int month) method and using that in the constructor, you can get rid of most switch/if statements.

Invalid dates

You chose to create a 01.01.2000 date in case of invalid date elements. Professionals will instead throw an IllegalArgumentException.

As a Java beginner, it's quite likely that you haven't learnt about the concept of exceptions yet, but it's an important thing, an elegant way to tell someone who wants to construct e.g. a 31.2.2010 date that you can't give him that date as it doesn't exist. As a caller of a constructor or method, I always want to be informed about success or failure, and exceptions are a good way to do that.