Is a free vector editing software similar to Illustrator?
Yes, there are several. My go-to software is Inkscape mainly due to its stability: https://inkscape.org/en/
There's also the drawing tool from OpenOffice/LibreOffice if you feel like you need to create vector art in a Microsoft Word style interface.
If you need CMYK support there's SK1, though I personally haven't tried it so I can't vouch for it: http://sk1project.org/