Just ran into this problem. Before performing a search, click on any individual game page. The search bar there should work.
https://www.gog.com/forum/general/the_what_did_just_break_thread_20/post3421

The way to approach the Dreamlist, in my opinion, is to see it as a mini-game within the website to channel your nostalgia, hope and optimism. And, in some cases (but it won't be the norm), it can be used by GOG as evidence for the existence of potential buyers, in an eventual negotiation with a publisher to release a game here.

Yes, you just have to wait to see and hope that your dreamlist gets voted a lot to be able to enter as one of the candidates that will be chosen by GOG to be published in their platform in the near future.

Unless you're talking of small indies that they're actually unaware of, or (and in particular) of games that have been submitted to them and which they have rejected in the past, it's not GOG who makes the choice, but he publisher.

Except in the rare case where the publisher is dead/gone, such as is the case for so many shareware titles.

Or not so rare case for old games, yeah. But in those cases the question becomes where did those rights end up. If they did end up somewhere, in full, it's the new owner who makes the call. If not, well, see all the rights hell cases...
Speaking of shareware, seems like there's a book.