Yep, it's pretty common for people who can become pregnant to keep a package of emergency contraception in their room. In fact, it's something many places, us included, suggest people include in their safer sex kits. The reason for that is if a situation arises where EC is needed, it can be helpful to have it right their where you need it, rather than having to add "go to pharmacy" to the list of things you need to do while stressed. It also means you can take it right away, which gives it the best chance of working. EC does expire, but it has a decent shelf life, and if it does a person can just throw it away and replace it with a new one.
As for whether having EC on hand makes a person less likely to use a condom, I'd say that depends a lot on the person. Some people might try to use EC as their main method of birth control, even though that is not the recommended way of using it. But I think it's safe to say that most people keep it on hand as, well, a plan B in case their chosen method of birth control fails (or in the event that someone chooses to assault them without using a condom).
As for getting just a few birth control pills from a friend, you're right that doing so is not an effective way of preventing pregnancy. Birth control pills need to be taken every day to be effective, and it can take up to a month of use before they're fully effective (that's why we and many other places recommend backing up with condoms for at least the first month of the pill). This article does a really good job of explaining why that is: Three questions about taking the birth control pill (and plenty of answers)
. Too, it also wasn't sound of that person to take a medication she hadn't discussed with her healthcare provider ahead of time (and it also could set her friend up for issues, since she'd then have a pack of pills that was missing some days).