You will be listed as the owner, administrative and billing contacts. PrimeServer is listed as the Technical Contact. InterNIC WhoIs listing below. Yes, you, the customer, will be responsible for paying the registration and renewal fees for your domain. You will receive an invoice by postal mail and email approximately 1-2 weeks after the domain is registered.
More information regarding InterNIC registration fees is available at InterNIC's site.
InterNIC has taken a hands-off approach to handling prior and pending trademark names when registering new domain names. In most trademark cases, an infringement can take place with words that sound similar, are spelled slightly differently, etc. With NIC you can have a trademarked name in your domain and they will register it to you without doing any search. Not very good news if you spend lots of time and energy promoting your domain name, only to have someone come out of the woodwork and try to take it. There are several court cases pending that could change how NIC awards domains.