It is the same knife.

As far as presenting evidence goes, it may as well be the same. But the actual knife they used are different, they have the same shape and look because they're part of a standard issue toolbox for the space center

In case 5, Pearl reveals that black psyche locks guard secrets the person isn't consciously aware of, yet in the previous game, Kristoph Gavin had them, yet he was obviously aware of his secret! It doesn't make any sense to me.

Kristoph was incredibly possesive of his secrets the point of paranoia. Its possible that during his time of the 7 years, he mannaged to force his real motive for murder so far down into his subconscious that he, at the time, almost completely forgot about the motive. It certainly seemed at the time that Kristoph was attempting to feign ignorance. However, at court, when he was faced with evidence, he was forced to recall the details of his murder.
Alternatively, the source that Pearl read is only one interpretation of what they could actually be. Perhaps somewhere there's an alternative explanation for what the black psyche locks could also be: a secret so dark that the locks themselves turn black. In both occurrences, the secrets hidden have to do with a murder so perhaps that is another possible criteria for the colour of the lock.
And then the most likely explanation is that Capcom simply added the definition while ignoring the specifics of the previous black lock sighting (although that seems a little peculiar, seeing as I seem to remember Phoenix recalling Kristoph's locks after seeing Athena's)

are suggestions of possible paycuts made by prosecutors

Every killer will be spoiled in the episode's intro sequence. I definitely hope not and if that's the case, I'll try to look away.

It was only for case 1 and 2 that showed who the killer was. The rest of the cases dont

What does Athena call Pearl in the localisation of Reclaimed?

Wait so ok, didn't Myriam give the tape to the police because she has tapes everywhere? BUT then later they say that Hugh was given it by Professor Means to give in to the police? Or was it that Myriam gave it to Professor Means who gave it to Hugh who gave it to the police?
idontunderstand

Myriam claimed to have recorded it, but she didn't. That tape was taken from a different recording anyway, and Means gave it to Hugh to give to the police.

First, it is said that Prof. Means' staff has been used to look like Phoenix's arm on the statue; that implies he wouldn't have it until the body is being moved at the center of the stage, so during the mock trial. However, at the very beginning of the case, we meet Prof. Means right before the mock trial, in the Lecture Hall... and he does have his staff at that moment. Does it mean the body would have been moved before the mock trial started (and also before Means' speech, because Juniper is inviting him to get ready to give his speech before Athena and Phoenix leave the place), but after the announcement inviting the students to get in the Lecture Hall? I don't know, the timing looks way too short for me. Not to say it simply contradicts the facts, as they're stated.

Another thing: what about the awl? Maybe I forgot that part, but did the blood actually belong to Courte? Was it the real murder weapon, or it's nothing but phony evidence (and the murder weapon is Prof. Means' staff/spear)? That piece of evidence seems to have been completely forgotten during the second day of the trial.

Because that would mean he brought the murder weapon to the trial when he could have brought a clean staff/spear.

Does she call him a phantom in Japanese version?

Nah, she just literally calls him a ghost/monster. The term for "The Phantom" is a different one, since it's written using the kanji for "lost spirit".