Is there any way to remove 512 character limitation of a newsfeed in Sharepoint Server 2013?
There is no out of the box setting where you can extend the 512 char limit. However there are a few workarounds to accomplish this, but I'm not sure that's what you want. Maybe a blog feature would suit your needs better? Or if you're using Yammer, which is a tool much better suited for greater lenght posts.