Short-cuts for Duplicate, Clone and Copy/Paste: see this. Duplicate is Control + D.
To create customized shapes and objects, path in Inkscape is worth learning to use.
Change background color: open File/Document settings (shift+ctl+D) and select the color from the Color/Background tab. Use FF in the transparence setting of the RGB color picker to make the color solid (00 means completely transparent).
Edit complicated equations: I use the Tex Text plugin to edit math equations in Inkscape. There could be some version compatibility and dependence issues if installed in a wrong way. Just follow the online instructions to install and use the plugin. Once installed, a preamble defining dependent packages and macros can be included for LaTeX equation rendering. Most likely, errors–if any–can be solved following some online instructions. An instruction to install TexText 0.7 on Inkscape 0.92.2 can be found here.