Noob neural network question--variable number of features?

Hello,

I'm taking Andrew Ng's Coursera course and feel like I'm understanding the material well. We've just finished classifying images of hand-written digits using a single hidden layer neural network. I wanted to try applying this workflow to another image identification problem, then realized:

1. I don't know what to do if the images of interest have different numbers of pixels. Must I crop or rescale into the size used for training? Or is there a way I can feed a variable number of inputs into an NN?

2. Are there good image datasets available to practice image classification problems?

Thanks!