1) Is a Ph.D in Biological Sciences frowned upon by technology companies, or is it out-weighed by the Ivy League tag?
If you're applying for a job at a company where you don't know anyone, your CV will end up in the hands on an HR person. I'm not in your field, but I think there's a considerable chance this person won't be able to see how a PhD in biological sciences connects to a CS/applied math job. The Ivy League tag will (on average) give you an edge, I suspect that to the uninformed eye, it might still look like you're applying for a job out of your field. Note that this doesn't make things impossible. They just make things more complicated, and you'll have to do some explaining on your cover letter.
If you use your connections to refer you to a hiring manager, then you'll skip HR and things will be easier in every respect. This is what you should always try to do, even if you get a PhD in CS.
2) How big of a role does the type of Ph.D play in the hiring process in the U.S., compared to what you actually did (thesis focus, publication record, software)?"
For a pure research position, your publication record is what matters (and people publish more in the US than in Europe). For an industry job, your work experience weighs in and people want to know what you can do (your publication record is important to show you can produce innovative ideas, but the industry generally requires a strong component of practical, hands-on experience).