I would love to be wrong, but at this time I believe the answer to both questions is no.
After the first year, your wife might be able to begin the citizenship process (definitely after two years), and she could (legally) work while she is studying.
Even though you are married, you may be able to come only as a tourist and stay for either 90 or 180 days (if your tourist permit can be extended), but I'm not sure about that). You might try to find work but you would not have a DNI. If you overstay your tourist permit, you might be able to begin the citizenship process at the same time as your wife.
PS: Your wife would probably have to renew her student visa after the first year. I'm not sure how "concerned" migraciones might be (if at all) about the fact that her husband has overstayed his tourist permit...if that's the case and they are aware of it.