One thing that troubles me is why does a non profit open source browser buy premium offline ad space to promote itself? There's a huge "The new Firefox" ad in down-town Berlin.
Mozilla makes money from having users — it may be open-source but the developers still need to be paid. They don't have a captive audience like Windows or Google.com users to advertise on, so public ads seem necessary.
ELI5 example: The more users you have, the more the search providers (like Google, Yahoo and Yandex) may pay you to be the default search provider in a certain region.
Not really "per search"... the deals are negotiated for N years. If that was per search Mozilla's finances would not be in such good shape, which could actually help them focus on chasing the right targets.