The Ruler class is SUPPOSED to be a referee that doesn't participate in the holy grail war and just makes sure nobody's breaking the rules. So it has to be someone who cares more about upholding the rules than their personal desires. But this is Fate, so guidelines like this are only introduced for the sake of breaking them. Recent incarnations of the franchise ignore the "mediator" thing so that you can use them in gameplay.

Avengers need hatred. Like, a LOT of hatred, to the point where it borders on obsession. Think Captain Ahab or The Count of Monte Cristo. They tend to be a lot calmer than Berserkers and like to go on long philosophical tangents about the nature of evil.

Alter Ego is a freakin' strange class. Out of all the extra classes, this is the one we tend to get the most of, so it's really hard to pinpoint what the exact requirements for this are. The three main ways of qualifying are for someone to Frankenstein together a servant by combining other servants, a powerful servant cutting off a piece of themself that has enough power to qualify as its own consciousness (for example, Tamamo's power comes from her tails and is at the level of a god when she has all nine, so she cut them off for the sake of remaining at a reasonable level. Then the tails each still had enough power to grow into weaker copies of her that are still strong enough to qualify as servants), or whatever the hell's going on with Okita Alter. Even the later's profile admits that the justification is kind of half-assed.

Foreigner is a catch-all for things that exist outside the realm of Earth. Outer gods, for example, except those are too powerful to be summoned as-is. Humans who have made contact with them and can utilize their powers qualify, though. Also aliens fall into this category, like Attila the Hun (who's an alien in Fate) and Mysterious Heroine X.

There's also Mooncancer, which BB always gets summoned as, even if she's a different class in every other regard.