I'll do my best here but please remember this is ultimately my opinion/limited experience:
(1) the student was given non clear advice;
This is subjective, a court wouldn't be expected to, or be capable of, judging what constitutes 'clear' advice to a PhD student.
(2) the university has acknowledged that provoked severe distress in the student due to lack of supervision and communication;
Bear in mind with a court the judge will likely have heard cases of bricks being thrown through windows, knives being pulled, or years of abuse; this doesn't make the stress of any individual experience less or more significant, but you do need to understand there's a (depressingly) high bar there around claiming for stress. If you're not claiming for stress, but a procedural failing, this doesn't help your argument.
(3) this stress is scientifically proven to affect the rational adjustment of a person, who becomes unable to estimate risk/reward ration and tends to ask and trust the opinion of an "expert" (aka Dean of Department);
It would be a court hearing, not a PhD viva. The way civil courts work they will want to be in and out in 15 minutes. It's also for this reason having multiple points isn't a strength; you want a single clear (ideally procedural) failing on the universities behalf, because they will find for the defendant if you don't provide one. Basically a judge will look (in about 10 minutes) for a) what was promised/contracted, b) the evidence this was not delivered. a) and b) need to be crystal-clear to win as if things get vague/complicated/compounded, it's in favour of the defendant.
(4) a deadline was coming;
Seems irrelevant.
(5) the observations reported timely by the same student (since 18 months) affected the viva; (6) in the entire university websites and regulations there is no written information on the possibility or procedures to postpone (so, actually, he didn't have really other options in that moment).
You may get them on this. Anything with regulations/procedures/breach of contract is where you would want to focus. If there's a lack of information that they're obliged to provide, or you were treated unequally due to them failing to provide you with information, you can win a case. Basically, the vast majority of cases won against universities are them failing to provide services as advertised or to-contract. As I mentioned in my previous post, though, they are aware of this and have stealthily and unethically been amending/carefully wording what they advertise and contract to protect themselves.
