In the field of medical imaging ,can we use U-net for segmentation, CNN for the feature extraction, and transfer learning based pre-trained alexnet, resnet, vggnet models for the classification.
I think UNET is perfect for segmentation(it is made specially for medical image use case and give very acceptable results depending on the quality of images) , for feature extraction start by testing one of the pretrained network you mentionned (resnet50, Xception give good results) and for classification better to look for testing RandomForestClassifier or SVM (i prefere RF)
Mostly the first and best choice for image segmentation is U-net-based architectures. The following paper has reviewed U-net and its variation for medical image segmentation: Preprint U-Net and its variants for medical image segmentation: theor...
A brief answer to your second question would be yes! CNNs can automatically extract existing patterns in an image which makes them perfect for feature extracting.
Lastly, it is so convenient to use pre-trained networks for classification. Even it may seem surprising when figuring out that in many medical papers, they use models pre-trained on ImageNet, which is totally irrelevant to medical images say MRI of the brain! In this case, they are benefiting from learning the basic patterns by the earlier layers.