Well fellas, I should clear some of this up. I know this seems like pure excuses (because well, it is, but honest ones from before the mission was released) but here's an explanation for some things. Still, I do not claim this to be an in-depth story, but SWEGTA did miss some things so here I'll address some things. Some things he didn't notice and some were my fault for getting lazy half way through. Also I had these plot explanations thought out, but didn't really show them in the mission well and maybe expected too much implication.
The context for Pete being outside, is well, Jimmy walks outside of the dorm and Pete happens to be there. You find out why when you talk to him. Jimmy would walk out of the dorm like that any other day so it should seem normal. Pete was waiting outside to tell Jimmy something and Jim noticed him so he walked over.
The reason Pete ran off was he actually needed to find his crack dealer. He was hopped up on drugs too so that is why he runs fast. The mission was meant to be like 2x longer, and after you killed Beatrice you were going to meet Gary to ask wtf is up with Pete, and you two would go to find Pete and get in a drug shoot-out with the new ultra spud-gun and possibly a police shoot-out for the lolz on top of it. A shoot out because Pete fails to pay his drug debts. And the reason Pete doesn't tell you where Algie is is because he's in a rush for drugs.
Gary then when you talk to him, doesn't know where Algie is. But he has a theory that if you need to find him, you will have to be the one to find him, and it must be inside you but you just don't realize it. To find the knowledge of where Algie is, you need to go on a spiritual journey through your mind. How will you do this? I dunno, so let's ask a teacher!
Galloway, Jimmy asks him because Jimmy and Galloway have a better relationship than most teachers because of the favors Jimmy did for him. Galloway still being a drunk ol' bastard currently has some booze, and well when you get enough of a buzz... you may see things. So Galloway thinks giving Jimmy the booze will help him see his vision that reveals where Algie is.
The first attempt is a failure however... Jimmy just had a wicked dream about bunnies. Galloway doesn't take him to the hole, but Jimmy being drunk ends up in the hole. He was too wasted to remember how he got there so it's blacked out, but we'd assume it was chasing bunnies to the hole to begin with.
Galloway follows you but, he just let you do your thing and when you calmed down (as in, stopped punching the air) he talks to you. It was a failure you two find out... so... let's try again!
This time you have a stupid lil dream that shows Algie at the funhouse. He silently and creepily says "Jimmy..." then after a few time shouts "JIMMY!!!". So you figure... algie? Funhouse? He must be at the funhouse!
You go there, and you see Algie is there with his dog. Why the funhouse? Because Algie wanted to be there with his dog. He wasn't just going to stand around the library and wait for Jimmy, he wants to enjoy his day, so he goes to the funhouse while he waits. Why doesn't he go to Jimmy in the dorm though in the first place? Well, Jimmy is sleeping and we all know Jimmy has some intense anger issues, so waking him up would result in some heavy shit. So he told Pete to tell Jimmy about him. But god dammit Pete... you and your drugs couldn't tell us where he was before running off!
Now you think... cure ebola? Da fuq? Beatrice is smart... she may have something! Maybe she's at the girls dorm...
She is! Doing what? Standing there. Why? Because she's a lonely fuck and was just standing outside of the dorm. If she was in the dorm she'd probably be picked on by Mandy anyway so she just stepped out.
She's got one! But dammit hatrick.... took it away. To the Gallo-mobile!
Now arriving at Hatrick's party, we see one of the partiers made his way outside. Perhaps he was waiting for someone at the gates. He notices young Jimmy... a bit young for this party, so he doesn't let him in. Jimmy uses his wits to outsmart (punch) him. Then they fight to the death! knock-out.
Now it's time to go get our paper back... but as all cliche bosses are, they wait until you kill all their minions to come out because they are cowards. Hatrick lets you deal with all the partiers before showing himself.
The house has glitchy AI, but is still fightable.
Hatrick, I wasn't even aware of the apologize bug, but he was just at a party.... maybe he got a lil drunk at the party and well... couldn't even remember what the fuck was goin' on.
Now... back to Beatrice! She's in the same place because she has nothing better to do than study, and if she goes in to study Mandy will just torment her. You obtain the supposed cure.
Now... to Algie! Algie and his dog are a bit more mobile, they decided to go to the library and leave the funhouse while you were out doing your thing. He's there because he got bored of the funhouse.
You cunt! The "cure" killed his dog! Fight!
Oh shit... you fuckin' wit da nerds? Well... Earnest doesn't like you messing with his clique. here he comes with his new Ultra spud gun. A semi auto-matic potato-generating (infinite ammo) spudgun that deals additional damage! You have a few seconds to kill him before he readys the gun and starts firing. If i made him fire right away... the player would totally get butt fucked hard. Now you have the ultra spud gun after beating him, and it indeed is semi automatic so you can just spam the fire button and deal tons of damage to Beatrice upcoming.
Beatrice... what'd you do? You'll die for trying to kill everyone! To what SWEGTA said, she wants it done now, she doesnt want to wait and allow the ebola to spread and get to more people, so she must exterminate NOW.
At this point, Jimmy helped Algie (or, tried) and saved the world from beatrice, so he fulfilled his duty. He however didn't check on Pete's drug habbit, because I got lazy.