1 MDN keeps an accurate list of compatibility per-element. Here's the list for SVG: https://developer.mozilla.org/en-US/docs/Web/SVG/Element/svg
Feature Chrome Firefox (Gecko) IE Opera Safari
Basic support 1.0 1.5 (1.8) 9.0 8.0 3.0.4
2 Keep the style in your SVG - it'll make it easier to swap out for other SVG images later. You want to be able to quickly update your svg. This one is more a matter of preference.
3 I wouldn't get in the habit of tweaking vector-art exported from CorelDraw by hand. You may think to run it through a minifier, but hand-tuning is almost certainly more work than it's worth.
Here's the first minifier Google gives me: http://petercollingridge.appspot.com/svg-optimiser For cases where you're not inlining, you can give .svgz (compressed svg) a shot, which will make it significantly smaller: https://graphicdesign.stackexchange.com/questions/24797/when-should-i-use-svg-or-svgz-for-my-web-graphics
4 Hmm, other tips - well good on you for using vector art on your site. Too many web devs/designers take the shortcut of doing everything in raster. While that gets you a nice looking image for a demo, in the long run it's really hurting your site. With ubiquitous tablets + phones, pinch + zoom is everywhere and your images need to scale nicely.
Personally, I've never loved the idea of inlining svg - I've always preferred saving as .svg and src-ing it like an image. I see why you are inlining it, though, as you're using some hovers.