Inkscape's only export option, png, is unacceptable because it ignores the transparency settings and displays the image at full opacity. But I can use Gimp to convert the png to pdf, which restores the proper transparency settings.
I think you have some wrong information there. Inkscape's PNG export does respect transparency. Maybe you've been thinking your image viewer is displaying transparency, when it isn't? Or maybe there's some other explanation. But you can export an image with transparency as PNG, and the PNG will have those transparent areas.
If Inkscape's PNG export did not contain the transparency, then GIMP would not be able to extract the transparency from it, to create the transparent PDF.
However, if I were having something professionally printed, I would not provide them a raster format. I would provide them whatever vector format they will accept. Because often, they will take the raster image, and trace it to make it vector, and maybe even charge you for it. You would have to ask your printer some very, very specific questions, and make sure they give you non-bs answers, to find out if their equipment is actually using a raster image, or if they are converting it to vector themselves.
For vector images, resolution is irrelevant. Just provide a vector file, make the card the size you want, and you don't have to worry about resolution.
Every printer has different equipment and different preferences. So you can't generalize what all printers are asking for. You need to specifically ask the printer who you plan to use or hope to use. When we have people post what formats their printer wants, very few of them accept any raster formats. And those who do, usually will convert them to vector. Well, at least that's what I've learned by reading messages. As I can recall, most of them want AI format, although I suspect they probably get more PDFs than anything, because PDF is a little more "universal". But that's a guess on my part.
I don't know about your other points. But I suspect that each printer has their own routines and preferences, for those points as well. I think you should have a good relationship with a professional printer, where you can ask questions, and feel confident with their answers.
I guess color business cards (well, more than one color, let's say) do cost a lot, don't they?
You should easily be able to create a business card in Inkscape, and with a good printer, who is honest and you feel comfortable with, it should be no problem getting it printed. I guess in some areas, getting an honest dependable printer might be easier said than done. I don't really know, but we have heard some stories!
Anyway, you don't need any other software (except for the color, if you want color). If you need CMYK color, use Scribus. It supports SVG and is also free and open source. I can give you a tutorial, if you like.
