Mr Fitzgerald accused the Home Secretary of failing to inform herself and properly consider these risks before deciding in October last year to permit extradition.
He said she had also failed to request an undertaking from the US that Mr McKinnon, "a seriously disordered person", would be repatriated to serve his sentence in the UK, or request that he be given bail pending trial.
Hugo Keith, appearing for the Home Secretary, argued that the minister had acted within her powers and extradition would not be oppressive or unjust.
Mr McKinnon's risk of mental illness could be mitigated by treatment in the US - "otherwise one would be arguing that no-one with severe or moderately severe mental suffering could ever be extradited".
Lord Justice Maurice Kay and Mr Justice Simon said they hoped to give their decision on Friday.
Mr McKinnon has always admitted hacking into the computer systems in 2001-2 which the US government says cost $800,000 (£550,000) in damage.
He has always said that he had no malicious intent but was looking for classified documents on UFOs he believed the US authorities had suppressed.
Speaking on Thursday, Professor Simon Baron-Cohen, a leading expert on Asperger's Syndrome responsible for the diagnosis of Mr McKinnon said: "If, as I believe, the crime was committed through naivety and through an obsession - in this case with computers and trying to find information - without any intent to deceive, without any attempt to hide what he was doing, we should be thinking about this as the activity of somebody with a disability rather than a criminal activity."
Mr McKinnon's legal team have sent a request to the Director of Public Prosecutions (DPP), Keir Starmer, for him to face trial in the UK rather than the US.
The DPP will give his answer in four weeks time and the court heard today that the Home Secretary had agreed to postpone Mr McKinnon's extradition until the DPP had considered his response.
'Ray of hope'
Speaking on Thursday, his solicitor, Karen Todner, had feared he could be removed to the US within days.
Speaking outside the court Mr McKinnon said: "It's been a good day overall. For a change it's slightly good news - a little ray of hope."
If his legal team can persuade the DPP to try Mr McKinnon in the UK, he would face a three to four year sentence rather than a potential 70 years in US courts.
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