Yes you can, simply use this function in init hook: ap_register_user_page($page_slug, $page_title, $func, $show_in_menu, $public);
I think this is due to other search filters. Question embed and question as comment will introduce in 2.4
Check this image:
I told you to read docs. Its in appearance->menu->anspress->user notification. Please avoid duplicate questions.
https://gist.github.com/rahularyan/0b37680c1a24c1e78baf#file-gistfile1-php
Edit AnsPress base page and set page template as AnsPress page.
Its look like you have modified content.php?
You are using image in category, so its usual. If you want small icons you must use font icons. You can check available fonts in askbug here: Font icon
AnsPress is not responsible, check other plugins.