Can I save only some VGG19's layers into a .H5 file?
after creating the model you can create another model as below ( I created model till 8 layers)

model = Model(vgg19.input, vgg19.layers[8].output)
model.save('./style_transfer/st.h5')


You can also use post-training Quantization techniques to reduce the size of the model to deploy in mobile/IoT devices. please check tensorflow documentation here