Can I replace my Shimano Nexus 7 with a Nexus 8 hub? My 2 year old bike has a (damaged) Nexus 7 IGH, it started running heavy and I can't find out why.

Rather than getting it fixed I'm considering replacing it with a Nexus 8 hub, as they supposedly of higher quality (apart from the obvious extra gear). 

Obviously I need a new 8-speed shifter to do this, but it looks to me that I can use the old roller brake assembly and the chain (very little obvious wear).

Can anyone confirm this?
Depends what roller brake model you have.

Looking at the Shimano 2015-1026 component line up document you can see what components work together. (Very useful current line up web pages here, with links to PDF docs for previous years.) 

You presumably have a Nexus SG-C3000-7R hub. That should be paired with the BR-IM81-R, BR-C6000-R, BR-C3010-R or BR-C3000-R roller brakes.

The Nexus 8 is the SG-C6000-8R or SG-C6010-8R hub which works with the BR-IM81-R
or BR-C6000-R brakes only.

The PDF doc is very long, but you can search for the product numbers to find the Nexus 7 and 8 sections.