As far as we know, there's no conceivable way that anything could interact with the spaciotemporal realm (I'm glad you remembered that because it's a whole lot shorter to type) without existing as part of it. I mean, there's matter and energy that we know exists in it that doesn't interact with baryonic matter. I can't imagine something completely outside of it that's able to interact with it.
The mind-body problem, as far as I know, has been settled. The overwhelming consensus says that the mind is the body. There's no separation between the brain and the consciousness. Consciousness is a product of our bodies. So that wouldn't be evidence for a way in which an outside being could interact with the inside world. If something has an effect in the spaciotemporal realm, it has to be in some kind of contact with it. I don't see any way around that.
That's true, there's no number I can put on the probability. Though we can only use all of the evidence available to us. We have to consider what we know when determining probability, we cant use what could be. If new evidence comes along, we can include that in the calculation. Thus far, the probability is extremely low. That said, it may be extremely high, but we can't know that yet.
I hope that bit about helping the world didn't come off as a criticism, because I'm hardly up in a high tower existing solely for the betterment of society. I just get frustrated with the state that philosophy is in. Most people view philosophers as spaced-out bearded men who don't really create anything of value, and philosophers have brought that stereotype upon themselves. There are important issues people face every day, corrupt families, governments, war, and it's the job of the philosophers to attack those problems. But instead, there are academics still focused on whether or not we can trust our senses. It's like if doctors in the midst of a great plague spent all of their time and energy on a virus from space that will come down in an asteroid and infect 1 person every 1,0000,0000,000 years and result in giving them a runny nose for a couple days before they get better. And not only that, they're debating on whether or not that virus exists.
Coffee fueled rant you say? Ignore my 100+ posts in this thread, I've never had coffee in my life.