For persona, start with 5. 3, 4 and 5 all take place within the same universe but the stories are not connected. The gameplay is at its most polished with 5.
Hash algorithms don't take an input and make it smaller. What they do is, they take an input, plug it into a mathematical formula and that outputs a string of text of fixed size, the actual size being determined by the algorithm used.
There are a few key factors people take into account while making a hashing algorithm:
collision resistance. It won't ever be possible to make it completely resistant, so they aim to make it unfeasible to do with the foreseeable future of technology. Many technologies we rely on, such as TLS, rely on hashes for verification purposes, so collision resistance is very important for that.
irreversibility. This is a big reason why it doesn't simply convert big output into small output (the other being that hashes can actually be bigger than the input data itself). Information is lost in the hashing process to the point where you can't take a hash and unhash it into the original data.
reliability. The algorithm must create the same output given the exact same data.
predictability, like you said, but only kinda. While it is true that a requirement is that an attacker must not be able to derive even part of the original data, a lot of the onus here is actually on the user to not use predictable inputs when using hashes for secure things. As said before, a hashing algorithm must give the same output when given the same input, so someone using, let's say a hashed timestamp for something secure is being a moron.
Get this: their digital licensing protection scheme was entirely client side. Which meant anybody with a hacked 3DS could just request any game they liked directly from the eShop.
That is what we call an attack, or a vulnerability. It isn't supposed to happen, and at the point where it does, that algorithm becomes cryptographically insecure and should not be used.
I see what you're thinking though, as it would be such an old hash that collisions must be known, right?
Well unfortunately, what we are dealing with here is encryption, not hashing, and hash collisions do not apply as an attack vector to encryption.
You could in theory try a cryptographic attack on the encrypted data but then you run into a few other problems:
you're effectively distributing a DRM bypass tool, expressly forbidden under DMCA
Attacking even the likes of RC4 takes considerable compute time on modern systems
If you do crack it, you legally can't store it, which compounds problem number 2.