Is there a way to open .ai, .eps and .svg files in Linux natively? Gimp can save in svg, but am not sure about the other file types
You have to try Inkscape! This is a very good Vector graphics program. The official homepage!, or just use the version in our repositories.
Extract from homepage:
Inkscape has sophisticated drawing tools with capabilities comparable to Adobe Illustrator, CorelDRAW and Xara Xtreme. It can import and export various file formats, including SVG, AI, EPS, PDF, PS and PNG.
So it should be just what you are looking for!
As a complement: to just simply view a svg file, main internet browsers can do the job.