I think any race conspiracy gives power to Nazis and immediately puts Jewish people at more danger. Making both US news and Zionism antisemitic. That's all I've put together.
I really should've asked this in a post long ago, I just feel embarrassed about not knowing.
Read The Empty Wagon by Yaacov Shapiro (Or listen to his podcast) to answer the second question. This is not exactly how he would describe it: One way to conceptualize it is that the Zionist project, being a predominantly Western-Christian obsession, is just the most recent of the Crusades, and this time they deputized a bunch of Jews to be the point of the spear. The most basic way it is antisemitic is that it endangers more Jews than any other thing in the world today.
The us media supports it because Israel is a long-term us project centered around oil, trade routes, and military and surveillance technology and the us media is controlled by companies that have a huge interest in such things.