How to add a white border around an illustration?

Can you show a screen shot of one of your files or give us a size?  You could create a mask so when your file is trimmed you have a white border.  You could size the PNG down so there is white space around the artwork.  A few different ways to do the same thing.  That's why it is important to discuss the details of the project, so you get accurate recommendations.

if you need it to be like a rectangle or circle you can use the basic shapes tool to draw it the select it with the selection tool.

make the fill color to (None) and the stroke color to white with the stroke width you need.

If you need to draw irregular path, use the pen tool or the curvature tool.

if you want to see the white color go to View>Show Transparncy Grid. if you make this or not, when you export your file as PNG the white artboard will convert to transparent.