www.ckdev.info/twt/things-to-do/drink

I'm starting to like K2 and what it can do (this is my first installation) but it's so complex and, for a new user, unintuitive in setting it up. And the documentation isn't detailed.

I can make an article and do this, but it must be able to be done with K2 I assume. The out-of-the-box styling is ugly, but I don't know where to alter it. Firstly I want the images much bigger - currently it's 100px and I've changed every setting I can find that specifies 100px without making a difference. I also want to get rid of that nasty background that seems to be color #F7FAFE. Again, no idea where to access this setting.

The image needs to be reuploaded so it can be resized to the new size.
The background is generated from CSS in this rule.
Remember to override the k2.css file. Move it to the css folder of your template.

www.ckdev.info/twt/things-to-do/drink

I copied the whole k2.css file to templates/<my_template>/css, then edited it. Nothing. I thought I'd done according to your instructions. I also added the whole CSS snippet you quote to the end of the template.css file, but that had no effect either.

The snippet I quoted is where the background is being generated.
There is no need to copy it, you need to edit it.