Does saving photos on iPad from Photo Stream save the full resolution?
All photos on Photo Stream are stored in the cloud in full resolution.  When they are pushed to an iPhone, iPad, iPod touch or Apple TV, they are downsized to make the best use of bandwidth available to those devices.  So when you save a photo which was taken by another device from Photo Stream to your iPad's Camera Roll, it doesn't receive the full resolution photo.  

However, if you take a photo with an iPad (or iPhone/iPod Touch), you will have a full resolution version of the photo in Camera Roll.  You will also have a full resolution photo pushed to Photo Stream and on any Mac or PC which is synced with that Photo Stream account and a downsized version on any other iOS devices synced with that account also.  

From Apple Support:


  On your Mac or PC, your photos are downloaded and stored in full
  resolution. On your iPhone, iPad, iPod touch, and Apple TV, your Photo
  Stream photos are delivered in a device-optimized resolution that
  speeds downloads and saves storage space. While actual dimensions will
  vary, an optimized version of a photo taken by a standard
  point-and-shoot camera will have a 2048 x 1536 pixel resolution when
  pushed to your devices.