In order to get all of the challenges done as quickly as possible there are a few tips I can give. However, it's still a slow process and look forward to a lot of aggravation with the inability to skip through the dialogue.
First, like the other solution states, throw up a tab in your favorite browser and navigate to this page.http://familyfeudinfo.com/
Bring up the Find feature, and as the questions come up in the game, do a find on some of the key words/phrases. This is a lot easier then using the built in search function on the webpage.
The second tip I can offer is to always let the AI guess first in each round. If their guess is not on the board, MAKE SURE YOU ALSO GUESS WRONG. This will end the round and start the next round. However, make sure you always guess first and guess the #1 answer on the 4th round, as that is always the last round of the game. The AI won't always guess wrong (almost always does on Easy but rarely does on Hard), and sometimes they might guess the #1 answer, but I've never seen them choose Play. They always choose to Pass, so you're not wasting much time and the payoff could save you minutes each game. With how annoying this game can get, saving minutes can be saving sanity.
During the Fast Money round, it can get hectic trying to find the questions on the website and inputting the answers before time runs out. Don't sweat it. Just hit the Xbox Guide button to pause the game and take all the time you need!
Please either comment below or send me a Personal Message if you have any comments or improvements to this solution.