Erlan, it's a custom code modification to display another tab instead the Latest tab as default.
I can give you instructions how to set Featured tab as default. You need to modify /ow_system_plugins/base/init.php file.
Find the line which contains: array('list' => array(OW_Route::PARAM_OPTION_HIDDEN_VAR => 'latest')))); code and replace the "latest" on the "featured"
After changing the code make sure you've cleaned browser and site cache. To clear site's cache enable DEV_MODE. Follow the instructions:
https://docs.oxwall.org/plugin-tuts:enable-debug
If you still need to set the Search tab as default, you can make a post in the custom code modification forum, probably some community member will assist you with that.
Concerning the fields on the Search form, you can hide them selectively.
For example, if you do not want to use Username field you can hide it in Admin Area> Users> Profile Questions> Profile Questions tab. Hover mouse over the Username field and click Edit option. Uncheck "On Search" option. In the same way you may rename titles of profile questions. Be note, if you change profile question title, it will change for every page where it's used.