Yes, photos imported into an iPad do get shared through Photo Stream. This feature is mentioned in this Apple KB article.
The 1000 picture limit is a per hour limit. Apple says (in the same KB article) that…
If you exceed one of these limits, your uploads to Photo Stream will be paused temporarily and you may see a notification message on your device. Your uploads will resume automatically once you no longer exceed one of the limits (such as the following hour or day).
In addition to the 1000 picture limit, there are further limits…
- Uploads to My Photo Stream per day: 10,000 photos
- Uploads to My Photo Stream per month: 25,000 photos
These limits can not be circumvented (as far as I know) by having your computer constantly sync to Photo Stream.
This Apple KB article explains Photo Stream resolutions:
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. Panoramic photos can be up to 5400 pixels wide.
According to the same Apple KB article as the previous, yes, Wi-Fi is required for Photo Stream to work (emphasis not mine).
On an iOS device, new photos you take will be automatically uploaded to your photo stream when you leave the Camera app and are connected to Wi-Fi. Note: My Photo Stream does not push photos over cellular connections.