Much better to use a CMS—especially as coding is not your focus. It would take years to learn this properly.
I would like to have a lot of control over the appearance on the site, is there a particular CMS that would support this (and my other requirements)?
Basically all of them allow you to change the styles, but some make it easier than others. Some have rather complex, contorted template systems that make is hard to change the layout, while others are very flexible and leave complete control of the front end coding to you. IMHO, ExpressionEngine is the standout example of this.
Can I get inside the CMS and make changes using HTML/CSS?
Yes indeed. As I said, some make it much harder than others to do this.
Do most CMSs support responsive/adaptive site design?
Usually, styling, appearance and behavior of this sort is up to you, not the CMS. So it's up to you to create / style the temples to behave in this way. Again, the better CMSes make this easier. If, for example, you use some junky old CMS that still works in tables, you are up the creek—though I suspect there are few, if any, that still do that.
At first glance, there are many things that appeal to me about Wordpress, is it heavy duty enough to support this kind of site?
Yes, but it's a friggin mess behind the scenes, and you have to hack it around to do anything other than blogging. I would recommed you check out other CMSes first before rushing into WP. [Runs for cover now that he's bagged WordPress ...]
If so, can I make manual adjustments to Wordpress using HTML/CSS?
Yes you can, but WP templates are a bit of a mess to work with ... harder than they need to be. Check out something like ExpressionEngine. It's a dream to work with. If you don't like the price tag, check out something like MODx or Concrete5.