First Question: Yes, all the images to be used for training have to be the same size. (at least for the last time I did face detection sample training. Should be the same here. If I am not wrong, there will be an error if the images are not of same size. But u can try it out and see if time permits.)
Second Question: Not really sure what you are asking here. But the classifier is not that sensitive as u think. A few pixels off the object of interest, let's say the hand for instance, if the little finger is missing a few pixels(due to cropping) and other images have few pixels missing for the thumb, etc... the classifier will still be able to detect the hand. So a few pixels missing here and there or a few background pixels added in, will not affect the classifier much at the end of the day.
Third Question: You should crop the image to consist of the car only for maximum result. try eliminate as much background as possible. I did a research based on samples with noisy background, black background and cropped samples with minimum background. Cropped samples with minimum background shows the best results in terms of false positive and false negative, from what I remember.
U can use object marker to do it: http://achuwilson.wordpress.com/2011/02/13/object-detection-using-opencv-using-haartraining/
The tedious way would be to use paint to resize all the image to the same pixel value after cropping.
This link should also answer your question: http://coding-robin.de/2013/07/22/train-your-own-opencv-haar-classifier.html
I also agree with GilLevi that there are much better detection methods compared to Haar, HoG, LBP cascade. training of the images can take days(depends on number of images trained). If you really have to use the cascade methods and you are looking to minimise training time, training with Haar-like features takes much longer than with HoG or LBP. But results wise, I am not really sure which will ensure better performance and robustness.
Hope my answer helped you. Should there be more questions, do comment.