They face charges of conspiring to commit racketeering, conspiring to commit money-laundering, copyright infringement and aiding and abetting copyright infringement.
A date for the extradition hearing has been set down in August.
Dotcom won bail after a month-long legal battle but was told he was not allowed online. His fortune has also been seized.
Today, Dotcom's lawyers argued the German-born millionaire needed access to the internet to properly prepare his defence.
He also sought use of the swimming pool at the rented $30 million Coatesville mansion where he and his family were living at the time of the raid and the ability to travel regularly to Neil Finn's Roundhead Studios in Auckland to finish an album he is working on.
Judge David Harvey granted him access to the internet, a 90-minute swim each day and two trips of four hours each a week to the studio.
Crown lawyers, appearing for the US Department of Justice, expressed "a level of scepticism about the success'' of such a recording.
Judge Harvey also indicated there was no real reason why Dotcom and his family could not move back into the rented mansion but did not make a ruling on that.
At present the family lives at a smaller mansion nearby.
Dotcom's associates were granted a meeting once a week with Dotcom in Coatesville.
