@EODK9 Your svg looks fine for printing. I would convert it to CMYK and save a pdf as "press quality" before printing. I also like Doug's suggestion of adding a darker silhouette behind it in case there are any white spaces between the shapes where colour might be missing. One area that caught my eye was the white "crack" at the very bottom of the image (you can see a little empty triangle), but the silhouette behind it will hide any of this. If your image is printed small enough, chances are, any little white space won't even be noticeable anyway.
If you're just using the svg for brochures and flyers, there will be no problem with digital or offset printing (But first convert to CMYK, pdf).
As far as logos, I don't recommend using detailed illustrations as a logo. This is where you can also run into issues with various media (printability - such as embroidery, silk screen, letterpress, etc; and scalability/visibility).
If you want the colours more simplified, instead of using a conversion app that you purchased, you can take the original photo / jpg, and bring it into Illustrator. Click on your jpg image after placing in Illustrator. Then choose "Image Trace." Go to Window > Image Trace to view options, and play around with the selections . You can choose how detailed you'd like it. Once you're happy with the preview, you can expand the image to vector. However, your image should print fine as is, especially once converted to cmyk and saved as press quality.
Your svg is only 541 kb, which is an okay file size for web... but if you prefer to use a raster image (not a bunch of vector shapes), you can make it into a png - a single image with a transparent background - for web use. Only make the file dimensions as large as you need it to be, as scaling up will lose quality in raster images.
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