The first thing to understand was that this Stack Exchange site graduated from beta to a full site two and a half years ago. The design was set up at that time, and at that time Android v3.x aka Honeycomb was the newest version of the Android OS. You can see the thoughts from Jin, Stack Exchange's designer in this post: Design ideas for Android.se Site. (follow-up design talks: Design mockups for final site theme, New Design Launched & Roboto is the new Droid.
The honeycomb-ed background is obviously based on the idea of Android Honeycomb, and in my opinion is nicely understated, just adding a bit of texture to the page. It's also physically isolated from the input boxes, which are either surrounded by white or black, so I'm not sure what the relevance of being nearly the same colour as the border of the input box has? You could certainly make an argument that Honeycomb is a fairly old version of Android now, but at the same time re-designing the site every time a new version of Android releases is probably a bit more work than Stack Exchange have time for while they're still busy launching new sites every month, all with their own unique designs.
The "green-ish question title and other texts" points exactly to Android, for the reason that you yourself mention, that green colour is #A4C639.
this Meta site is not using Android's bot logo properly
If you have a look around the Stack Exchange network, "meta" sites always use a desaturated/greyed-out/monochrome version of the main site's theme. The site/Android logo on the main Android.SE site is based on #A4C639, the logo for the meta site is just a grey version of the same logo. Android's branding guidelines allow for this sort of modification, monochrome-ing a logo is very different from making it pink with yellow polka-dots.
that said, do you have any specific suggestions for how these things could be improved?