Downloading large photos from Photo Stream on iPad
On your first question, this is what the Apple My Photo Stream FAQ says:


  What resolution are My Photo Stream photos?
  
  On a Mac or PC, your photos are downloaded and stored in full
  resolution. On iPhone, iPad, iPod touch, and Apple TV, your photos are
  delivered in a device-optimized resolution that speeds downloads and
  saves storage space. Dimensions will vary, but 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. Panoramic photos
  can be up to 5400 pixels wide.


On the second question, the Photo Stream criteria for deletion –not the images you took or saved with the device, which stay indefinitely on the Camera Roll– is defined as follows in the same document:


  How long are My Photo Stream photos stored in iCloud?
  
  The photos you upload to My Photo Stream are stored in iCloud for 30
  days to give your devices plenty of time to connect and download them.
  
  How many photos are stored in My Photo Stream on my devices and computers?
  
  My Photo Stream pushes all your photos to the My Photo Stream album on
  your devices and computers, and manages them efficiently, so you don’t
  run out of storage space.  
  
  Your iOS devices keep a rolling collection of your last 1000 photos in
  the My Photo Stream album. From there, you can browse your recent
  photos or move the ones you like to another album to keep them on your
  device forever.