So his home work is shimapan and ero audio books? He must be a professor of lewd.

Monki said:

So his home work is shimapan and ero audio books? He must be a professor of lewd.

The context of the shimapan is shown in the other 2koma in this "chapter" on ComicWalker or Seiga, but it's not much context.

MrSusher said:

The context of the shimapan is shown in the other 2koma in this "chapter" on ComicWalker or Seiga, but it's not much context.

Is there context behind why he's just listening to porn while they're studying?

I was about to release this as a typeset 2-koma but then I decided to check it. Your second speech bubble is a made-up rewrite.

スピーカー で 流すなり して,
気 を 利か せ なさい よ ホント 使えない わ ね.

In the second speech bubble mayuri is saying that the headphones are leaking like speakers.

Notice how in the first panel, there are small bubbles around the boyfriend which imply sound is leaking.

Also notice that there are no speakers anywhere in the background, therefore the boyfriend simply increased the volume of his headphones to make fun of mayuri comparing his headphones to speakers.

tinkerhell said:

I was about to release this as a typeset 2-koma but then I decided to check it. Your second speech bubble is a made-up rewrite.

スピーカー で 流すなり して,
気 を 利か せ なさい よ ホント 使えない わ ね.

In the second speech bubble mayuri is saying that the headphones are leaking like speakers.

Notice how in the first panel, there are small bubbles around the boyfriend which imply sound is leaking.

Also notice that there are no speakers anywhere in the background, therefore the boyfriend simply increased the volume of his headphones to make fun of mayuri comparing his headphones to speakers.

At its most literal I interpret スピーカーで流すなりして to mean　she's telling him to "let/make [the sound] 'flow' through/with [a/the] speaker(s)". 流すなりして to me sounds like she's telling him to do it. And "speaker" can just mean the phone's built in speaker. She's also chastising him for not being tactful and letting her hear, and between that and the volume being suggested in the second panel I don't think it makes sense to turn up the earphone volume instead of letting the sound play through the phone's speaker.
My Japanese might not be great, especially when it comes to grammar, but I see nothing there to suggest such an interpretation. I don't think anything in the phrasing is comparative or alluding to the earphones being like speakers and I'd expect to see something like 漏れる rather than a more deliberate sounding 流す if it really was trying to convey the sound being "leaked".

Makes me wonder if it's her panties on the table.
That her panties was taken due to an earlier situation.

Liggliluff said:

Makes me wonder if it's her panties on the table.
That her panties was taken due to an earlier situation.

Yes and yes. You can see it in the links in the commentary.