If I kept two rats in a cage a male and female, would the male kill the female for dominance? And also do Wild rats come in packs in houses?

If this was the other way around, I would say it'd be okay for a couple of days. Hamsters have a pretty advanced digestion system and can get bloaty and sick when fed the wrong things. But never fear if you google hamster food you can find some more ''organic?" supplements until you can make it back to your local store. Rats/Mice on the other hand are made to hoard their food. They don't stuff it in their cheeks, although mine likes to sometimes it seems, they like to hide their food. Doing this they burn more energy and need a higher energy/protein diet.

I don't buy rat food, I make my own. I did the same with my hamster too with the store bought mix. Here's a list from my memory you can give hamsters that you may have around the house.

Carrots
Apples
Granola (Good for teeth!)
Cooked red meat (like hamburger meat)
Water Chestnuts
Nuts
Shelled almonds (more fun!)
Bread/Toast (My friend made peanut buttered toast for her hammy)
Fish (fully cooked!)
Eggs (Scrambled/Boiled no fried)
Cheese (in moderation)
Mealworms and crickets (you probably don't have these but for future reference :) )
Dog Biscuits (Try to stay away from some high in protein, and it's good for their teeth!)

Hope that helps!

They can be very friendly if raised from babies. They need to be caged at night or they will cause you grief.

Mice will survive just fine on their own outdoors.

An aggressive rat can bite the cat if it is a docile cat.

Wood is made up of cellulose fibers and when digested turns to sugar in the rats digestive tract.

Cover the cage at nite so it is dark inside and then the hammie should sleep also.

You can put a piece of clear plexiglass to divide the cage in two. They can still see each other but with no shinanagans

Watch and see when the rat goes for food. Then set out the food and watch so when it comes out shoot it with a BB gun.

This is probably way too late, but...

It will take some effort on your part. You can buy a safe (non-poison) rodent repellent on Amazon. That's only part of the solution, though: you need to make sure that there are no openings to the outside that a mouse could get through (an adult mouse can squeeze through a hole a bit smaller than a dime). If you live in an older home, it may have roof ventilation that is open to the outside; mice can climb very well, so to open vents would need be covered with screen.

You can also get live traps - bait them with some peanut butter or sunflower seeds, and leave them before you go to bed where you see there has been activity (gnawed objects or droppings). The next morning, take the traps to a park or meadow/woods and let the little intruders go. Try and relocate them a good distance from your house, or they'll find their way back. IMPORTANT! Don't keep a mouse in a live trap any longer than you need to 8-10 hours max) or the stress will kill them.