To register as a developer to the Google play market you have to pay a fee of 25$(100$ on the appstore), to cover my loses I have to make some money out of my app, so I need to advertise ads, hence the INTERNET permissions (almost every free app that has nothing to do with the Internet has those permissions because of ads).it.
So, you're advertising and making a profit. Then at the very least, this thread counts as an advertisement, which is in violation of PEEL's TOS.
Now to the "copyright and intellectual property".... WHAT ???? this app was made entirely ,fully and completely by me, all questions were written by me (took me a few months), Matt Groening should be thanking me for releasing this app, because it shows the power of this show to have so many apps of it.
Background art, along with images and sounds from the show were created by and are owned by Matt Groening or his commercial partners. He certainly shouldn't be thanking you for stealing his stuff. You should have asked for his permission before using them.
If I'm not mistaken, simply making a trivia app related to a copyrighted work isn't violating that copyright, because it can't really be claimed that a bunch of trivia questions take substantively from the work itself; otherwise, a hell of a lot of bars and companies that host trivia nights would be in serious trouble. There are plenty of trivia apps (including some Futurama ones) for sale for the iPhone, and Apple hasn't taken them down for infringement. Now, if the app uses images from the show (which this app does appear to be guilty of), or for that matter, any video or audio from it, then that potentially becomes a different story.
This app does use images and audio from the show, and is unlicensed. For the author to make a profit from this is considered theft.
It should be noted that PEEL and CGEF (especially the latter) are probably technically in violation of copyright laws as well, particularly since CGEF uses banner ads to derive some financial support. Of course, by now FOX has learned to be a little more lenient with fan sites for their TV properties.
As I understand it, CGEF has always been in contact with either FOX or Groening's offices, and has had their "unofficial support". Whilst this is the sort of thing that could be withdrawn at any moment, with FOX requiring a licensing fee and whatnot for future operation, CGEF (and by extension, PEEL) have the tacit consent of the show's owners. This goodwill is in part dependant on PEEL not being a haven for or repository of links to unlicensed content, bootleg merchandise, and the ever-feared illegal downloads of the show itself.
As for advertising, PEEL and CGEF don't make a profit. They manage to generate some of the money that it costs to pay for the server and bandwidth. Apps, on the other hand, are something that it doesn't cost to have hosted and downloaded to people's machines. If this app takes off, the $25 it cost to register it with Google isn't going to be a repeated charge, whilst the advertising revenue is going to keep coming in (making an app a potentially very lucrative thing), meaning that the author stands to make a decent profit.
Plus, the sorts of "free" games that come with advertising installed can be incredibly annoying (and if I was somehow foolish enough to download one of these, I would end up giving it the lowest possible rating based on that alone).
Now to your fears of "god knows where", every app uploaded to the Google play store are tested by them(it is only visible to the public about 2 hours after the developer's upload), so please don't worry for "god knows what", you can feel safe downloading it.
Since that's failed to prevent other data mining apps from being made available on Google play as "free toys" before, I don't think that should re-assure people. In fact, Google themselves are notorious for collecting as much information about an individual as they can (although Google do tend not to sell much of that data to third parties. They keep it for their own purposes).