Most of your questions already have answers so I will just link to them:

• Is there any difference between the GPL and AGPL for code executed in the browser? For code in the browser, there is no practical difference between GPL and AGPL 3.0. So yes, you have to distribute the JS source code when using this library.

• If a part of the client-side code is licensed under GPL, does the server-side code have to be under GPL as well? You don't have to distribute the Java part (the server part) as the two are generally considered distinct works.

• Is putting a page with javascript in it considered a redistribution As you are mentioning, you are indeed distributing the library (but not as source code) thus you need to comply with the terms of the license (and distribute the non-minified version as well).

• Yes, such a matrix exists: http://choosealicense.com/appendix/

Most of your questions already have answers so I will just link to them:

• Is there any difference between the GPL and AGPL for code executed in the browser? For code in the browser, there is no practical difference between GPL and AGPL 3.0. So yes, you have to distribute the JS source code when using this library.

• If a part of the client-side code is licensed under GPL, does the server-side code have to be under GPL as well? You don't have to distribute the Java part (the server part) as the two are generally considered distinct works.

• Is putting a page with javascript in it considered a redistribution As you are mentioning, you are indeed distributing the library (but not as source code) thus you need to comply with the terms of the license (and distribute the non-minified version as well).

• Yes, such a matrix exists: http://choosealicense.com/appendix/