Is there a summary of each singularity I can read? (SPOILER)

Solomon make a wish to grail, to become a human
Fou (one of Beast of Calamity) use it's power to revive Mash

There's always the type-moon wiki.

Well here's the deal:

- Solomon was summoned in that past Holy Grail War by Marisbury Animusphere, won, and wished to "become a human." He was essentially reincarnated as Romani Archaman. They aren't quite the same person because Solomon is fundamentally inhuman, he was born solely to be the King of Israel and was never allowed to hold human emotions or sentiments. They have different personalities and perspectives.
- Goetia is not Solomon, he is the King of the 72 Demon Gods. They dwelled within Solomon's body and essentially dragged it back to life after sitting in Solomon's corpse for some time after his death. They've just been using his body all this time, but it does give them access to his Magecraft and NPs.
- In one of the cutscenes you skipped Goetia used Solomon's Third Noble Phantasm, Ars Almanel Solomonis (the bands of light we've been seeing this whole time) to attack Mash. She used her Noble Phantasm, Lord Camelot to block it. While she successfully protected you, her body could not stand the sheer heat and was incinerated.
- After this, Romani turns up in the following cutscene. Since Goetia threw away the title of "King of Mages" when he burst out into his Beast I form, Romani "picks it back up" and manifests as Solomon. Now it turns out that out of Solomon's Ten Rings of legend that he supposedly received from God, Goetia only possessed 9 of them. The tenth one was dug up and used to summon Solomon for the Holy Grail War, and is currently in the hands of Romani/Solomon.
- With all ten rings present, Romani/Solomon is able to use his First Noble Phantasm Ars Nova (which Goetia did not know the name of). Using this Phantasm recreates the event in legend where Solomon returned his ten rings to God, and in this instance it is symbolic for Romani/Solomon giving up his everything, all of his life and achievements. Romani/Solomon disappears from existence completely, even from the Throne of Heroes and the position of Grand Caster.
- The now non-existence of Solomon causes Goetia and the other 71 Demon Gods to start collapsing since they are now mortal and no longer united in purpose and mind. Some of them self-destruct, others are destroyed, some "refuse union" and cut themselves off from Goetia, a few even side with the Heroic Spirits and are killed by the other Demon Gods.
- Anyway, Goetia is killable now so you go and kill him.
- Back to the Mash question. It turns out that our friendly neighborhood Cath Palug (Fou) was actually Beast IV, Primate Murder. He's a creature that gains magical energy anywhere humans are competing with one another for power, and he uses this power to stay at the top of the food chain. He was in the Tower of Avalon with Merlin for a while since he can prevent himself from becoming powerful and monstrous by staying isolated from humanity, but Merlin (being the bastard he is) tossed him out of Avalon and told him to go experience beauty. That was several hundred years ago, and he's been experiencing beauty and sucking up magical power all this time (though not enough to become monstrous). He uses this power to accomplish a miracle beyond True Magic, resurrection of the dead. Though in reality he cheats a bit by "transferring his future" to Mash. Mash revives and the entity that is Primate Murder ceases to exist. Now Fou is just a little animal.

I think that about covers it. If you want nitty gritty details go watch the cutscenes.