@JoeWeb cheers for the extra pair of eyes on the site. The mobile version is a bit of a permanent ‘work-in-progress’. At the moment the search box is set to display:none on mobile as otherwise it part obscures the header image and looks really crappy.
As I said, I never see ads at all as I use blockers on all my browsers. But I think what you’re seeing sounds about right. AFAIK Google ‘reserves the right’ to slap ads on your search results but that doesn’t necessarily mean they’d always do so. I’d have thought only for suitably ‘keywordy’ searches.
Re: DuckDuckGo. although I use them for my day-to-day web searching, I decided to opt for big bad Google on my own site, just because it was the only one out of the three I looked at [Google CSE, DuckDuckGo Search Box and Yandex Site Search] that allowed you to embed the search results within your own site.
DuckDuckGo and Yandex both take you back to their own sites to show you the results which feels a bit ‘broken’ to me. DuckDuckGo say they do so because “…we do not have the syndication rights to allow you to host our results on your site…”, which is presumably because they pretty much just act as an anonymiser for search results from other search engines. It’s a pity Yandex don’t allow better integration. They could easily do so as unlike DDG, ‘they are their own man’ in this respect.
Correction: Yandex do allow you the option to display search results on your own site, but require you to have a dedicated search results page to display them on.