The New Tab layout is dynamic. Depending on browsing history, items will be added, moved or removed. Items can be pinned in place to make sure they don't move or disappear.
Just checked my FF search options and Yahoo is missing from the list. It can be installed by clicking on, "Find more search engines." This is a recent fresh installation, about a week old, so the defaults are probably intact. The list of search engines, in order, is: Google, Bing, Amazon.com, DuckDuckGo, eBay, Twitter, Wikipedia.