1.Your niche is an umbrella under which you can write a blog. Since my niche is how to heal from anxiety,I've written blog posts on how to overcome social anxiety and what foods to eat when you have anxiety.
2. I would second Cherry's definition of a blog, and add that I think it's always helpful to add some of your personal experiences within your niche. that way people can see that you're a real person and this builds trust.
3. Pick a blog and a niche that you have some sort of personal connection with. That way writing about it will be enjoyable and not a drag.
Hope this helps

Let's see:
1.A blog is a discussion or informational website published on the net. (that is the formal answer)
2.You choose something your passion about,like cooking
3.WA says 1,000 minimum up to around 3,500. However, I have done my own research and some successful bloggers do 800-1,000 words. I know it has to be over think 300-500 words to get Google to notice. However, the article should take as long as it needs to take to get your information out there.
4. It what use under your website name. Like your website is "Fresh Fruit" you could in your tag line Cooking with Fresh fruits. It's just a space to put extra information.

I hope this wasn't too long and that it helps a bit.

Good Luck.
Be Blessed.