(1). Does the user have to have a user rights define in SQL 7.0 in order to read/write data in sql server?
yes, you should define user or role or inherit windows users

(2). Do I need to accquire an additional licenses in order to add more users to sql 7.0? I.E. I want to give three more people the ability to access my app. The app uses the sql 7.0 database. I was told that I can not simply create DSN connection to the database for sql. I would need to accquire two more licenses for sql. Is this true?
Depend on your license. If you buy standard server license with 5CALs you have to buy as many license, as concurent connection your user will make.