Question

What is difference between adding external jar and using library project in android?
can we extract jar from library project and import it as external jar in our main application?

Answer 1

What is difference between adding external jar and using library project in android?

There is almost no difference in achieving a task between these two except a minor digression. That is if you add jar, you have to go with whatever defined in that external jar and the features that jar provides can’t be changed. If you include library project, you can play with the source code and make changes to the features if you don’t want to go with the default features. Both have their own cons and pros.
As I said, by including library project, you can customize the features, but you may not know whether if affects any other things that depends on the feature you are playing with. But that’s not a big deal if you are very wary. Adding a jar wouldn’t let you customize but then again it’s easy to follow the pre-defined features :). Hope this helps.

For your second question: can we extract jar from library project and import it as external jar in our main application?

Not exactly, but you can. See this great answer given by CommonsWare with many restrictions.