Is there a way to modify the order?
You could potentially do this by creating a custom action that uses the API (which supports ordering by publish date, title, etc in ASC or DESC order. We don't offer this as an option in the UI. Just out of curiosity, why would you change the order of blog posts?
Can I make one or more posts sticky so they are always at the top?
Again, not out of the box, but you could do this by writing either a) a custom theme that displayed one or more blog posts at the top of the page or b) a custom action that does the same.
Quick question a few years later on Blogs, but I would like to display Blogs in our Space based on when they were modified, rather than when they were first created. Is this option available - I couldn't see it in the widget. If there was a way of overriding this in Jive 126.96.36.199, that would be ace!