"Legal address" is used often but it does not have any special meaning when it refers to a person's address. It simply denotes a place where you can receive mail and where the police can possibly find you if they happen to be looking for you. You should specify a place where you know you can receive some mail in the US. Perhaps, the university office responsible for your orientation and settling in? And then update your address as soon as you find a place to live.
A SSN relates only to a person and is not "connected" to any address. So there is no wrong answer there. (When you get close to retirement age, the Social Security administration will start to send you money to the address they have on file -- but you can worry about setting this address long in the future).
As for credit cards: Credit Card transactions as a part of the payment card industry's anti-fraud measures, links a "transaction billing address" to the cardholder's payment address. These must match up in order for the transaction to go through. So for the credit card address the most important detail is consistency.
You will not have any US credit history until you begin to make transactions in the US (or more specifically, establish a billing address and start to make repayments on loans). Your US credit history is a very important record for living a normal life in the USA. The record consists of name variants, addresses, accounts and payments associated with you over time - and the "Credit score" is just a simplified way of summarizing how good or bad your history is. If you pay your bills on time, you will have an excellent credit score. If you open credit accounts with numerous pseudonyms, move around a lot and pay bills more than 30 days late, you will have a bad looking credit history and a corresponding low score.
The "permanent address" universities refer to is intended to be your parents' address. This is the address the university will write to whenever they want to communicate with you after you have graduated. Although it is called "permanent," you can update this address any time you want so it does not need to be different from your ordinary mailing address.