Resize the canva: use the artboard tool or resize the page on the artboard property following this tutorial. This is helpful to generate correct page (like for poster making) size or remove white space when exporting to eps or pdf format.
Cut a part of image off from a bigger one for later usage: use the Clipping Mask tool following this tutorial or this. In short, once the correct shape of mask is put on top of the parent image, select both layers with shift key, the clipping mask tool can then be applied from Object > Clipping Mask > Make.
Add equations to an image: I use the tex text plugin for Inkscape to type render LaTeX equations in Inkscape and then copy the equation to Illustrator. The plugin might have some bugs upon the first run, but it should be easy to fix following online instructions. The plugin allows a preamble that includes packages and self-defined macros for the LaTeX render. There is actually an issue regarding the exported PDF so that I have to print the file in Adobe Illustrator directly. A better solution to include equations in AI is to copy equations from Microsoft Office PowerPoint with the IguanaTeX plugin. The equations copied might still look weak, but works better than Inscape 0.92.2 with TexText 0.7 if exported to PDF.
View artboards on AI: select the menu at Windows –> Artboard to open the artboard list window or press shift + O. Select the opened artboard on the list, and then one can delete one artboard if not needed.