Not directly-- would probably need an adapter. But Amazon also sells an "AmazonBasics 5.9 ft. (1.8 meter) High-speed HDMI to Micro-HDMI Cable" and in the "at a glance" box it says "Compatible with the new Kindle Fire HD models" and it looks like there is also a 10-foot version if you need the extra length. So if you've got an HD, there may be a solution.
The shorter the cable, the better the signal strength and the less data loss due to internal "friction" and flaws... However, in lenths of ten feet I don't think any loss of attenuation would be detectable.
No idea. Sorry. It was my understanding of HDMI cables that it's either good, or it's not. If it works, it's good. If it doesn't, it's trash. I might be wrong, but I was pretty sure that there's no tier of quality - if you get a cheap cord and it works, that's all you need. You can spend however much money you want on it, but it's not making any actual difference.
However, I understand things may have changed since I looked into it a couple years ago. But if I had to guess, I would say that the cheaper one is more than likely going to be just fine.
Yup - the research I did said that all HDMI cables are pretty much created equal, and what you wind up paying premium prices for is the packaging. I am using one of these from my cable box to my tv and another to connect my tv and dvd player. I assume it would work equally well with Blu-ray.