Hi Andy,
I am not able to replicate the issue where the blog detail is on the right side instead of center. It could possibly a skin specific issue. If you can produce the problem on demo.mojoportal.com, I'll take a look.
What many people do is keep the blog on a separate page, then use a Feed Manager on the home page to consume the feed from the blog and show the recent posts. However, if you want to try that, you should avoid moving a blog from one page to another after it already has posts. You could either create a new blog on a new page, or rename your current home page to blog and keep the blog on it, then create a new home page and move it into the home page location.
When creating a blog post, existing categories are shown as check boxes you can select. To create a new category type it into the text box and click the Add Category button. When you create categories and flag posts with those categories, it produces a list of categories with the number of posts in each category. There is a setting in the blog to show the categories as a cloud, if you check that then the size of the fonts for categories will be weighted according to how many posts it has. You can see this in my blog. In a CSS you could alter the width of the side column in the blog to make it wider may make it more cloud like than if it is in a narrow column. You can also tweak the font sizes from CSS.
Hope it helps,
Joe