ALSO. I think the question misses its own point. Responsive design happens in the CSS ( or at worst js) of a site. In other word it's the skin of it not the brain. CMSs deal in content. It is quite possible you could have a well coded WP theme, and skin it to be responsive. Sure, the worse the code organization the harder it would be to accomplish... but this would be the same issue with a poorly coded Joomla or Drupal template, or even static HTML.
This is compounded by the CSS frameworks you mentioned. What is it that you are trying to do, EXACTLY? Which is also the problem right there. WP doesnt know your intent, and 960 doesn't know your intent so they throw every class in the book at you and it becomes a substarctive process: what DONT I need? Ironically, in order to knwo what you don't need you need to know what you do need, at which point it would be just as easy to code from scratch.
Is it possible to edit the HTML and CSS in order to get a customized website to my liking/needs in the same way as coding a site by hand or do I have to settle with a theme made by someone else (most likely becoming a compromise)?
You could do that with ANY CMSs' AND premade template, as I said before. And again, the problem would be that you would have to be able to decipher what the original creators of the template were thinking in order to make effective tweaks.
2) I'd like to have a search function for the site (it should also search through the site's existing and corresponding mailing list archive) but am struggling to find solutions for this. I understand that Wordpress has a site-search built in, which includes a MySQL database for indexing the site. Is this correct?
Yes, WP does. But it I warn you it's no Google. WP search is basically a "string" search through the DB and, because it was designed for blogs, results are return in chronological order. You could write your own engine for WP (WP_DB_QUERY) and some knowledge of PHP and MySQL would be required... but then you could do that for any other CMS.