Can a basic user add new companies, people and deals?

Yes, any user on the account can add new People, Company, and Deals. People and Deal owners default to the user adding the record; Company records must be assigned by Executive users. 

If the Company owner is a required field then the user adding the record will default as the owner. If a non-Executive user adds a new Company and the owner field is not required, the owner field will default to 'none.'