how to check cocoAspell?

However, there are many applications that have there own speller besides cocoAspell. I don't know which does and which doesn't... so how do I check that my cocoAspell works?

Apps which use CocoAspell are the same that use Apple's own spellcheck: TextEdit, Mail, Safari, iWork, etc.

Thanks for the hint. Would TexShop or iTexMac2 need cocoAspell or they can pick up apple's own speller?

I think CocoAspell just adds more dictionaries to Apple's own speller, so that if an app can't use Apple's, it can't use CocoAspell either.

Hmm... as I understand, Apple's own has an engine called iSpell, while cocoAspell has a different engine called aSpell which is supposed to be better.

That may be, but I don't think an app uses one or the other, it uses both or neither. In any case, it's easy to test this by installing whatever app you are interested in plus cocoaspell and see what spell checking is available to it. Let me know what you find out.