1. A photo stored in the Camera Roll is permanently stored on your device (until you delete it). Only 1,000 photos are saved in the Photo Stream on an iOS device, so if enough photos are uploaded to your Photo Stream the old ones will be purged. (But a Mac or PC will save all of the photos in your Photo Stream by default.)

2. According to Apple, the downscaling does only apply on iOS devices — if you have Photo Stream set up on your computer, those photos will be full-resolution.

   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.

3. Yes — to delete multiple photos, just tap the action button in the upper right corner, select some photos, and tap the Delete button.

   

On iOS 7

1. Open the Photos App and make sure you are in the “Photos” section from the three icons at the bottom of the screen;
2. Look at the top of the screen and make sure the view is “Moments;”
3. Now you can tap individual thumbnails one at a time to select them, or you can tap the word “Select” that appears at the top of each grouping to select an entire grouping.

On iOS 6

1. Go to Settings → General → Usage → Photos & Camera;
2. Swipe on the “Camera Roll” entry;
3. A “Delete” button appears.

This solution does not work on iOS 7 (last tested on iOS 7.0.4). It is probably a bug.

Any iOS, but using a computer

If you have iOS 7, you can use Image Capture on your Mac to delete photos from the iPhone without importing them:

1. Plug the iPhone to your Mac with the iPhone cable;
2. Quit iPhoto if it launches automatically;
3. Launch Image Capture;
4. Select the photos you want to delete;
5. Click the red icon to delete the photos.