In the past species were limited by how far they could walk/fly/swim. Now humans can put any species anywhere in the world at any time (sometimes intentionally, sometimes not).
Well not that limited apparently since the whole world is populated. Humans speed up the spread of species (contributing to biodiversity lol) but the phenomenon itself is not new.
1. The rate of spread matters. Evolutionary adaptation is slow.
2. It's not just the speed, humans makes movements possible that were previously unlikely or impossible. Argentine ants are currently wreaking havoc across the globe. Do you think they would have ever found their way from Argentina to Australia and Hawaii without the help of humans?
1. Speed does matter, however high-speed changes in the environment are neither unnatural nor unprecedented.
2. If they are successful as invasive species, then yes most likely that would happen given enough time. Even the most remote islands in the ocean are populated with life forms that are too modern to be explained with plate tectonics. Nature has it's ways (besides evolving humans).
3. As you noticed humans spread all kinds of viruses, insects, blights and other unfortunate beings. Like them or not, they are as valid as a part of the biosphere as the chestnut tree.