You want to avoid making it look like it's actually "endorsed" by Google, or a product of Google's, despite interop with one of Google's products. The name can be an issue here, so you might want to come up with something spiffier and original, and point out that it works with Google's service elsewhere.

IANAL, but here's my take: anything men make is copyrighted. Getting rid of that is difficult or even impossible (depending on originating country and one's interpretation of the law)

Nothing physical can be trademarked. It's the idea of some features in a particular field that forms a trademark (in this case, the right-pointing triangle, the phrase "Google Play" in the 'app store' field) you break a trademark as soon as 'the typical consumer' might be confused who he is talking to.

So, the particular logo likely is copyrighted, and the idea behind it trademarked. If you redraw the logo (using some artistic expression; a 1:1 copy won't do), you are free from copyright claims, but may still be breaking trademark law.