Yes, I think it is possible. There is an option in some journal submission pages that a person is not an author but submitting on behalf of the group. Many journals do not have this option.
Yes, it is possible. In most cases the first author will handle the submission, possible revision etc. The corresponding author is either the first author or it is the professor, group leader etc. (basically the one who will be around when your (temporary) contract is over). See these examples where I handled at the time the manuscript in all stages and was not the corresponding author:
Article Competitive Adsorption Behaviour of Wheat Flour Components a...
Article Characterization of the Resonance Energy Transfer Couple Cou...
Chapter Characterization of helical junction zones in gelatin networ...