I didn't get everything but here's what I got. I also put the obvious stuff, for the sake of completeness. Feel free to correct if there are any errors.
Free hugs :
http://en.wikipedia.org/wiki/Free_Hugs_Campaign (I'm not sure what the link with anime is)
Nani ?! : Means "What ?!" in Japanese.
Desu : Means "(to) be" in Japanese, I think.
I hope this isn't a filler episode : A filler episode is an off topic episode where the plot doesn't advance. It is common to have those when an anime adaptation has catched up with the manga version and they need to wait for the manga to release new content. See
http://tvtropes.org/pmwiki/pmwiki.php/Main/Filler
I hope senpai will notice me : Senpai refers to fellow classmates of higher level or age. Or mentor/model/idol, etc …
I've read enough doujin to see where this is going : Doujin means "fanmade" (most likely porn fanfiction, in this context). It's a bit similar to the trend when people put a brazzer logo on a picture to imply something sexual.
It's time to duel ! : Catchphrase in Yu-Gi-Oh.
A wild skullgirl appears : That's how wild pokemons are introduced in the video games.
???bunshin no jutsu : Means "Cloning technique". Naruto's signature move.
Daijoubu : Means "Okay" in japanese, as in "I'm okay".
Mustn't run (I mustn't run away) : From "Evangelion". The protagonist (Shinji) says that regularly throughout the series.
Mada mada (Mada mada dane) : Means "No, not yet" in japanese, as in "It's not over yet", or "you still have a long way to go". Ryoma's catchphrase from "Prince of Tennis".
Zenkai : Means "Full Release" is japanese. It's a genetic trait that allows a Saiyan's power to increase substantially after recovering from near fatal injuries in "Dragon Ball".
Liftoff : I can picture Misato from Evangelion saying that at one point but I'm not sure if that's really a reference to that.
Beowulf sensei : Means "Teacher" in japanese.
Cerebella-chan : Affective suffix in japanese.
Eliza-san : Means "Miss/Mister" in japanese.
Neko : Means "cat" in japanese.
Parasoul-hime : Means princess in japanese.
Hentai : Means "pervert" in japanese. Refers to manga porn.
Another heaven coin closer to redemption : reference to Panty and Stocking with Garterbelt. It's a cartoon made by a japanese studio where two fallen angels must slay ghosts and earn enough heaven coins to be allowed back in heaven.
Art is an explosion : Deidara's motto in Naruto. He's an antagonist who enjoys blowing thing and views that as his own form of art.
All according to keikaku : Means "just as planned". Reference to Deathnote. see
http://knowyourmeme.com/memes/just-as-planned
Solar Flare : a move in Dragon Ball. See
http://dragonball.wikia.com/wiki/Solar_Flare
I choose you : Catchphrase from pokemon, when the protagonists chooses his first pokemon.
EDIT : Oh I hadn't see
@Grunt 's post, so a lot of that has already been said. The only new things are the obvious stuff and "(I) mustn't run (away)", apparently. Also Mada mada (dane) from Prince of tennis.