"What kind of medical stuff should we have in our dorm or house first aid kit?"
You can purchase a first aid kit with band aide, disinfectant etc from any pharmacy or large chain department store. If you were to have one medication in the house I recommend Benadryl. In case of a life threatening reaction such as a bee sting or food allergy in which someone is complaining that their breathing is getting constricted or their throat or face begins to swell, give two 25mg tablets and call 911 immediately.

"What do I use hydrogen peroxide for?"
Hydrogen peroxide can cause many problems for wounds. This solution only has one use and that is to bubble out debris from a dirty skin wound. If you get a road rash or other wound, pour hydrogen peroxide on it, wash it gently with warm soap and water and if there is a deep wound or cut cover it up with something clean and get to a doctor incase you need debriding or suturing.

"What are some of the bad things people do with hydrogen peroxide?"
Hydrogen peroxide is just water with an extra oxygen molecule so it has no ability to sanitize or kill germs. All it does is bubble like club soda. People like to put it on wounds that are trying to heal because they think that the bubbling is helping the process but it really only slows down the healing and makes the wound more likely to get infected. Do not put hydrogen peroxide on healing wounds or in your ears or eyes.

"How long do I have to get my deep cut stitched up by a doctor before it won't heal up very well?"
The general rule is that you have about 8 hours to get a laceration sutured before you have mixed or poor results. After this time, the wound will heal poorly and need to be debrided.

Here is what you should have in your house first aid kit:

Antihistamine tablets (Benadryl, Chlor-Trimeton)
Used for an allergic reaction such as inset stings and chemical irritants.

Band Aids, butterfly bandages, tweezers

Antibacterial ointment (Neosporin, Bacitracin)
Apply soon after cleaning cuts or road rash.

Tylenol (acetaminophen) (Alcohol warning!)
Used for pain and fever.
(see "Headaches" for more information and warnings about acetaminophen.)

Advil or Motrin (ibuprofen)
Used for inflammation following trauma or strain and used for fever and muscle pain.
(see "Headaches" for more information and warnings about ibuprofen.)

Good antibiotic cleaning soap (Hibiclens, Phisohex)
Used for cuts and scrapes.