A), these were not the tests I asked for, but OK….
B) Make sure you install the Xtreme Theme Support plugin, it provides additional features, including access to the Leagcy Admin similar to weaver II in Appearance > Xtreme Admin
If using the Customizer, you can also set the Customizer to WHERE mode instead of WHAT mode, that will organize options in a similar fashion as the Legacy Admin pages
1- You appear to have set the primary menu to “Fixed on top” change that setting to “not fixed”
2- The search on header can be hidden in Main options > Header > Header Area > Hide search on header
The space comes from an empty Site Title. If you do not want to see the site Title, you should still have one as it is important for search engines, but hide it using the hide site title option in Main options > Header > Site Title / Tagline section
3-The Widget title appears to have a font-italic setting, check what you have in Main option > Sidebar and layout > Individual widgets > Widget title font properties