Note that constructors cannot be synchronized — using the synchronized keyword with a constructor is a syntax error. Synchronizing constructors doesn't make sense, because only the thread that creates an object should have access to it while it is being constructed.

Which constructor Cannot be used for process Synchronisation?

No, constructor cannot be synchronized. Because constructor is used for instantiating object, when we are in constructor object is under creation. So, until object is not instantiated it does not need any synchronization.

Can abstract methods have constructor?

Yes, Abstract Classes can have constructors !

Of Course, abstract class can have a constructor. Generally class constructor is used to initialise fields.So, an abstract class constructor is used to initialise fields of the abstract class.