I am considering getting a slow-cooker. I leave for work by 8am, return about 4pm and feed my family dinner about 5pm. Can food sit in the slow cooker that long? Thanks.
Yes. A typical slow cooker's low setting ranges between 8-10 hours, which is within the range of your listed times.
All (or nearly all) slow cookers come with a removable ceramic bowl/insert that the food cooks in. Most families do most of the preparation in the evening, putting everything into that bowl, and putting the bowl into the refrigerator. Then when they wake up in the morning, they put the bowl back into the slow cooker and start it up.
Your bigger concern should be what size of slow cooker to get. If you don't fill up that ceramic bowl to at least 1/2-2/3's full, you can end up burning the entire dinner.
Easy, that's what slow cookers do. Not all recipes do well for all day cooking, but many do. Here's a little collection to get you started. Here's a Google search for all day recipes. The whole point of the Crock-Pot is that it gets food out of the "danger zone" (above 140F, 60C) quickly, but cooks the food slowly. There are tons of well loved recipes that will serve you well.
As for all recipe searches, look for strong reviews.
My grandmother says that if the recipe calls for 8 hours, she will sometimes cook it for as many as 10 hours and it comes out great. So I think it's fair to say if you cook for 8 hours and then leave on warm for 1 hour that it will be perfectly fine to eat.