Go here: http://strategywiki.org/wiki/Dead_Rising/Infinity_Mode
The page contains all the information you'll need to plan out an efficient 7 Day Survivor run. It features:
A schedule of every survivor and psychopath's appearance and disappearance, and the food they drop.
A list of all food that can be found around the mall
A list of safe places to hide in every area.
A list of clocks so you can tell the time – Frank's lost his watch in Infinity Mode.
You'll notice by reading the schedule that the survivors tend to spawn and despawn in groups (That is, at the same time, not the same place). So your plan of action should be, every time a new group appears, go around killing them and collecting their food. Once your inventory is full, wait until your health depletes and then use the food before moving on. If you've killed all of the survivors currently available, wait somewhere safe until a new group spawns, and only leave when you've recently healed yourself.
In order to get the most out of your food you will need the 3 health books, whose locations are listed in the article. You also need to know how many squares of health each item restores so that you do not waste anything. To find out, go here: http://strategywiki.org/wiki/Dead_Rising/Food
(multiply all values by 3 if you are carrying the books – which you absolutely should be)
If you are killing enough survivors and not getting hit excessively then you will be accumulating full-heal items faster than you use them. I am not very good, getting grabbed by zombies fairly often, but I ended up hauling around three pizzas I got on day 1 for the entire game. So don't panic about running out of food. In fact, don't feel that you need to kill absolutely every survivor, either. Many of them only drop a 1-health item, which is hardly worth the trip depending where they are. The guide helpfully highlights the ones carrying a significant amount of food.
Make sure you don't pick up larger healing items that are lying around the mall unless you really need to. As I just said, your inventory will likely be well stocked with the spoils from killing survivors. Picking up the static items just means you have to schlep them around with you instead of having them waiting for you in a predictable place. Picking up the smaller things that only heal 1-2 blocks (sans books) is okay. You'll use them more quickly so they won't clog up your inventory too much.
1.Heed the schedule's warning about the Food Court bug. You don't want to lose your progress half way through.
2.As it says, when you unlock 5 Day Survivor the laser sword is there right away, so use it. If you quit the game without dying you will not be able to use it in future games, though.
3.The page is wrong about this at least: you can kill people more than once. I've done it with at least Kent and the sniper family.
Anyway, this isn't too hard, just time consuming. Good luck and I hope the information is useful to you. Armed with exact knowledge about where and when every enemy spawns, I'm sure you'll agree this mode is a lot less intimidating than it might have otherwise been.