No, the president would need Congressional approval to have military units in Iran for more than 90 days. In practice presidents almost always ask Congress for advance approval, since having to pull out in the middle of an invasion would be rather embarrassing. The only exception that comes to mind is Reagan's invasion of Grenada, where the US military was in and out easily under the time limit.

So how does that limitation interact with non-personnel warfare, such as viruses and drones and spying?

Another exception is Libya where they're not considering it a military action.