When I create a new contact in a company, it automatically completes the address information fields (city, address, country, ...) from company fields. I also would like to automatically complete other fields like fax or telephone. Is there a way?
Yes, the standard functionality populates Contact Mailing and Other Addresses from Account Billing and Shipping Addresses respectively. If you want to populate Phone automatically you can make a workflow. It will auto-populate contact's phone from Account for new Contract records. So, all you need is just to leave the Phone field blank and it will be auto-populated after you click the Contact Save button.
Step 1. Setup > Automation Workflow Rules > Press Create Rule