Yes to the first assumption - with a caveat. To cross the width of space, their technology must be far ahead of ours. Imagine a modern army fighting one from the 18th century, and you could imagine what a tank, a machinegun, modern artillery or whatever other aspects would do.
BUT: There is also the point that we would fight locally, while they would need quite long-winded logistics. OK, they could mine asteroids, and if they have all the means of production, we would be f-ed.
Regarding the disease, well, any disease needs a host, and it is formed by evolution over millions of years to work on that host platform. Just imagine the aliens have a different interpretation of DNA, maybe for pairs forming a codon instead of three, or just different encodings of amino acids for their codons, and nothing would work. And that would assume that they are similar enough to actually have DNA.
What they could do, though, if they are technologically far ahead, they could probably synthesize a virus that is basically made to kill us off the planet before we know it.
So better not piss off any aliens that made their way to us... Gray lives matter!