See if it is holding a charge. Also, it might only charge properly with the charger it originally came with. The original Nexus 7 (2012) uses a charger that's rated at 2 amps. The second generation Nexus 7 (2013) uses a charger that's rated at 1.35 amps. If you're using a third-party charger that's rated less than the two I mentioned, it might might not do enough to charge it.
The 7 in Google Nexus 7 has not been openly mentioned to stand for anything. However, the recent Nexus tablet iterations (and to some degree, the phone as well) appear to refer to screen size. Both generations of the Nexus 7 have 7 inch and 7.02 inch screens respectively. The Nexus 10 has a 10.1 inch screen. The Nexus 4 has a 4.7 inch screen. The rumored Nexus 5 is supposed to have a 5 inch (or larger) screen.
It appears you can only delete the auto backup pictures from the desktop version of Google+, while leaving the picture stored in the Nexus 7. If you want to delete the pictures from the Nexus 7 itself, you can do this through the Gallery, Google+ (Photos dropdown), or the Photos app.
To change your Nexus 7 Battery, simply remove the back lid, and pull off the battery which is held by an adhesive, and replace it with the 4326mAh battery.
Yes, any of the Nexus devices can wirelessly print through Cloud Print and/or the HP Print Service plugin. You can get to the printing options from Settings>System>Printing.
It is possible, but it would a webcam app (ie: SimpleWebcamApp is one out there, available outside of Google Play however), terminal app/Terminal Emulator, a webcam that that has low-to-moderate power usage, and a USB OTG cable.
No, if you get them from Google Play you do not need a credit card.
You should be able to retrieve it from the Gallery and delete it from there. However, the image itself will still be kept with whoever you conversed with on their device.
The Nexus 7 does not have FaceTime. It's proprietary only to Apple devices. The Android equivalent is Hangouts, which can be used cross-platform.
If you have a wi-fi version of the Nexus 7 (1st or 2nd generation), which is the more common version of the tablet, you would just need to connect to a wi-fi hotspot, or connect to an internet service. If the Nexus 7 isn't finding a location for you, you can go to Settings>Wi-fi and locate the service you want to connect to.
The Nexus 7 tablet computer can download anything any other computer can download, too, local memory resources permitting. That is, a tablet computer with 4GB of memory will not be able to download a 12GB high-resolution video.
Downloadable data, however, fulfills a purpose. Textual data might be presented using the PDF file format, audio might be presented in an MP3 file, video in one of the many video formats.
The Nexus 7 (or any other device) may not be able to handle all of these formats. One could download it, but not use it. To use such data, additional programs ("apps") may be available.
Other data, such as executables aimed at a Windows operating system, can be downloaded but won't be useful on an Android operating system for the foreseeable future.
These devices can be "rooted" if you are familiar with the process. I believe the answer provided by a previous contributor to be wrong in the general case. However, the general consideration applies: if you do not know why, let alone how, you'd want to do something, do not do it.
The 2013 Nexus 7 is clad with Corning glass (scratch resistant) in the front, plastic plastic edging on the sides that transition the glass in the front with the soft-touch plastic back plate. It's narrower, thinner, and lighter than the 2012 original.
Here's a comparison, focusing on the 7 inch Nook HD (and not the 8.9 inch Nook HD+) vs. the Nexus 7...
The 7 inch Nook HD (discontinued on 6/25/13):
The Nexus 7 (2013):