I am glad you are enjoying working with the AtTask API and I am happy the documentation is helping. As for your questions:
1) You should be able to add a _Mod to any related field. For the below example I am using project:name from an hour search and only returning hour entries entered on a project which have "Test" in the project name. API Version should not matter for this functionality but if possible I would recommend using the latest version.
/attask/api/v4.0/hour/search?project:name=Test&project:name_Mod=contains
2) You are absolutely right and the documentation is backwards, we will fix this on the site shortly. The _Range value needs to be the higher of the two whether dealing with dates or numbers. Thanks for letting us know.
/attask/api/v4.0/hour/search?entryDate=$$TODAY-25d&entryDate_Range=$$TODAY&entryDate_Mod=between
The example above, which you provided, would be the correct way to use the between mod.
Good luck with your project and if you have any other questions or notice anything else amiss with the documentation on http://developers.attask.com/api-docs/ please let us know.