The search bar might be what you want. There is an option to turn it on in the settings.

Yeah, I usually download them from Pling. You could try NewAdwaita-slim.

There are many types of themes (look at what’s inside the theme folder) eg. cursor, icons, widget (gtk/qt), wm/de specific stuff (xfwm, cinnamon) etc.

The theme you downloaded might only have cinnamon folder, they can only affect the taskbar and the start menu. For the titlebar, you want gtk themes (the one with gtk-x.xx folder) and select it under Applications theme.

I think the ones listed under simplified theme are just presets of icon+cursor+gtk+desktop themes bundled together.

change your gtk theme

Remote input in KDEconnect, maybe.