Not sure if I totally get you, pretty much anything DRAWN in Inkscape will be saved as a vector. So if you were to import an image than draw over that with tools like bezier curve and saved that file it would save it as .svg thus a vector. As long as you don't draw the background and don't let your fill go beyond the outline of your character/asset the background should be an alpha (or at least it should be recognized as an alpha when you export the drawing as PNG, make sure you don't export the reference image with that otherwise you'll leave raster artifacts in there. But I guess by now you already figured that out.
I can only export the bitmap or save as a .svg for anything even close to what I want. Bitmaps don't zoom in, as shown in this image. Svg's have white backgrounds that I can't delete. Anytime I save a .svg file, even with the document properties set to have a transparent background, I get the white background when I try to upload an image anywhere. And, yes, I delete my reference image. I don't let my fill go beyond the drawing. It just doesn't work no matter what I do. Bitmaps are the only things that have no background, but I can't zoom in. In this image, it shows what type of files are vectors. Inkscape won't let me save any of these type of files other than .svg and it doesn't work.
Ah, well I think the white background you're referring to is the actual canvas correct? If so the reason that's white is because there's no reason for it to be an alpha. Considering a vector is a logical combination of lines and curves anything that isn't isn't read (of course besides the fill and strokes) by the program. So the background is actually transparent but rendered white I think. Bitmaps on the other hand do need a way to differentiate between white and transparent alpha. If you try to edit only a part of a bitmap that is full white, you can't with any tool or at least not in the place the lines where as the data of lines is no longer there. So it's normal to only be able to save .svg with a white background.
Also Inkscape is .svg only as it's an open-source program. .ai stands for Adobe Illustrator, .psd Adobe Photoshop and .fla Adobe Flash. Since Adobe is a commercial company with their own software, support and conversion of these filetypes isn't given to Inkscape for free so Inkscape sticks to the open .svg format. Most bitmap extensions used today are also open-source or free to use.
Hmm, I'm still not quite sure when you would want an alpha layer to be visible as one. By that I mean like a grey-white checker board. The actual canvas fully functions as an alpha, if it doesn't you can bring up the document properties panel by pressing shift+ctrl+D, at least on Ubuntu Linux/GNU but the shortcuts should also work in windows. There you should see a tab that says page, if it doesn't automatically select it, select it. You should also (in that tab) see "background:" with the background colour after it. If this is a checkerboard with white on the right side this is normal and it means the background is working like a normal alpha. The white on the right side means that if you decide to crank up the alpha is will take that colour and therefor you can't change that to an alpha but again, as long as your alpha is set to 0 the white colour (or whatever you want to set it to) doesn't matter.
However, if you only see one colour (no checkerboard) that means your settings are different so click on the colour and set the alpha to 0. I suppose this won't be in your case as when you exported it it used an alpha, so the settings should be as described in the first paragraph.
I also don't know if Adobe Illustrator (Ai) does have the option to make the canvas render as a checkerboard. But really only buy it if you're absolutely sure it's a necessity as there aren't any cases I could think of where it would be necissary to have it render as a checkerboard other than for aesthetic purposes while working, the export and data will still be the same as a vector made in Inkscape using Inkscape's alpha layer as it's set by default.
I hope this wall of text may have cleared up any misunderstandings and that Inkscape will have enough features to get you going with that, and if not that another program does have the feature you're looking for.
I have Illustrator CS6 and I've done my own artist logo and want to export in a vector. It is made with paths and I don't what format would be the best resolution to export it. Can anyone help with this please?
If not: Simply saving as an AI, PDF or SVG file will preserve your paths. Exporting to PNG is good for web viewing though. We always suggest doing at least 3000x3000, but it depends on what you intend to do with it. File>Save for Web is the easiest way to get a specific resolution; File>Export is best for printing, since you set the DPI instead.