SQL Server Service Accounts
To first address your questions: 


  The DB Admin team will remote desktop to that server and connect to
  SQL server using SSMS,not from their local SSMS. In that case do I
  have to have domain service accounts?


While I would not advise that a production database is administrated by running SSMS directly on the production server, these two items are completely unrelated.


  The application which DB support will have few hundred users
  connecting over network? In that case the default service account will
  be enough or do I have to have domain service accounts?


Again, these two items are completely unrelated.



You should check out Guidelines on choosing Service Accounts for SQL Server Services. The key parts of that, for you, are:


  During a new installation, SQL Server setup does not default SQL
  Server engine Service and SQL Server Agent service to any account. The
  account specification is required step for these services. For details
  on recommended secure accounts, refer to Books Online Topic Setting Up
  Windows Service Accounts.


and 


  When choosing service accounts, consider the principle of least privilege. The service account should have exactly the privileges that it needs to do its job and no more privileges. You also need to consider account isolation; the service accounts should not only be different from one another, they should not be used by any other service on the same server. Do not grant additional permissions to the SQL Server service account or the service groups. Permissions will be granted through group membership or granted directly to a service SID, where a service SID is supported. For more details please refer to Books Online Topic Setting Up Windows Service Accounts.


So based on that, you will need to specific accounts for the engine and agent, and I would recommend having discrete logins for all services which adhere to the principle of least privilege as per the linked articles from the quotes.