In the movie war of the worlds, Tom Cruise protected Dakota Fanning from Aliens. The Aliens were defeated by a virus in their energy supply. Fortunately the Aliens did not have access to a vaccine. https://en.wikipedia.org/wiki/War_of_the_Worlds_(2005_film)
In reality, no Earth virus would effect aliens and no alien virus would effect humans. As Dr. Robert Zubrin put it in his book "The Case for Mars", its like warning that a human could get Dutch Elm Disease.
We don't know that. Our biology might be able to defend, but it also might have tools that our bodies have never seen before, and are vulnerable to. And it's not just disease, it's probable that much, or all, of Earth biology would be toxic to aliens. Of course, if they came this far, they might choose to wipe out most life, and seed the planet with their ecosystem.
No. Organisms that can threaten humans have evolved in an environment along with humans and have specific keys to enable them to infect humans. As Dr. Robert Zubrin in The Case For Mars put it in the argument against back contamination. Claiming that an organism from Mars would destroy life on Earth is like claiming that because a Mako shark is one of the dominant predators in the ocean that it would be the dominant predator in the Sahara Desert if you released some there. You might as well claim that humans are in danger of contracting Dutch Elm disease.
We don't know that. For one thing, I was talking about aliens, not some wimpy bacteria barely surviving on Mars. How the 2 ecosystems might interact is not predictable. To use your example, it might be more like dropping a Mako into the community pool. As a rule of thumb, I would agree with you, but an exception might be no fun at all.
If you drop a shark on someone in the desert it will still kill them before it dies though. Saying that one organism cannot ever harm another when you don't even know what's in the universe is ignorant.