Where do I look to find information about how long a game will be on sale for? Since the redesign, I haven't been able to figure when something goes on sale, or how long it will be until it goes back to the regular price. Usually the news section had info about the current sales, but I didn't see anything regarding the current sales.

The new News section only hold 12 items.
You have to find older news on the forum, or use search engine like Google.
No, GOG's own search engine is damn useless and will find nothing.

I can't even find a link to the news section from the front page.

I know you used to be able to get a countdown timer when viewing a page for a bundle deal or a curated collection of games (ex. "On sale for the next 4d, 12hr, 20min"), but now it just does a search. Is that a bug or something?

Also, is it awful for me to say that the new site design/layout seems pretty terrible?

Only promo page have countdown timer now:
https://www.gog.com/promo/20181012_disney_week